First the card texts:

Notion thief:
If an opponent would draw a card except the first one he or she draws in each of his or her draw steps, instead that player skips that draw and you draw a card.

Leovold, Emissary of Trest:
Each opponent can't draw more than one card each turn.

So I have leovold in play, my opponent has notion thief. I cast Ancestral recall targeting me. Do I get to draw 3 or does notion thief still replace the draw but my opponent just can't draw them all so he draws 1 and the other 2 are dead?

Here's the 2 rulings from gatherer (for Leovold) that seem relevant, but at the same time contradictory:
Your opponents can draw a maximum of one card on each player’s turn. Subsequent card draws are ignored.
This would make me think he draws 1 off of my ancestral and other 2 are ignored.
Replacement effects can’t be used to replace draws that Leovold disallows.
Since notion thief is a replacement effect and leovold would disallow it, this would seem to extend to this situation and say that notion thief doesn't apply to the draws that are disallowed so my opponent would draw 1 and I would draw 2.

I dont think I'm applying the second one the way it was intended though, but the way its written that application certainly is reasonable.

My understanding is that Leovold only disallows your opponent's draws, so it does not apply to replacement effects that affect cards you would draw (like Notion Thief's). Depending on when you cast Ancestral Recall, your opponent will draw one card or zero if they have already drawn a card for the turn and you would draw zero cards as Notion Thief still replaces your draws, but the opponent's draws from the replacement effect are ignored.

A more interesting scenario would be if there was a Spirit of the Labyrinth and Notion Thief in play. If you cast Ancestral during your main phase after already having drawn a card, then Spirit of the Labyrinth would disallow those draws and your opponent's Notion Thief would be unable replace them according to the rule you cited. As a result, neither player would draw.

@ChubbyRain right on both counts I believe

Is there a general ruling or part of the Comp Rules somewhere that explains that replacement effects are replied before "can't" effects -- or vice verca?

@MaximumCDawg said:

Is there a general ruling or part of the Comp Rules somewhere that explains that replacement effects are replied before "can't" effects -- or vice verca?

Not that I'm aware of and that is why I'm wondering. The way the ruling is worded, a judge could reasonably state that since leovold disallows the last 2 draws of ancestral recall, the replacement effect from notion thief doesn't apply and I would get to draw 2 cards in my scenario. In plain English that is exactly what the ruling states. Like I said, I have a feeling that is not the intent and not what they had in mind with that ruling. But barring some other rule we haven't considered if a judge encountered this situation and stated that my opponent draws 1 and I draw 2 he could point to this as his justification and have the backing he needs.

@MaximumCDawg - 614.7. If a replacement effect would replace an event, but that event never happens, the replacement effect simply doesn’t do anything. From: http://mtgsalvation.gamepedia.com/Replacement_effect

This came up with the interaction between Containment Priest and Grafdigger's Cage, and MTGO handled it incorrectly (and I thought MTGO might have been right for a change).

@Khahan said:

@MaximumCDawg said:

Is there a general ruling or part of the Comp Rules somewhere that explains that replacement effects are replied before "can't" effects -- or vice verca?

Not that I'm aware of and that is why I'm wondering. The way the ruling is worded, a judge could reasonably state that since leovold disallows the last 2 draws of ancestral recall, the replacement effect from notion thief doesn't apply and I would get to draw 2 cards in my scenario. In plain English that is exactly what the ruling states. Like I said, I have a feeling that is not the intent and not what they had in mind with that ruling. But barring some other rule we haven't considered if a judge encountered this situation and stated that my opponent draws 1 and I draw 2 he could point to this as his justification and have the backing he needs.

It doesn't have really anything to do with what the rules are saying, but instead the issue lies with what you think is going on. Again, Leovold only disallows your opponent's draws. Notion Thief only replaces (in this circumstance) your draws. The actual mechanism for this is:

1. Ancestral Recall begins resolving
2. Cards are drawn one at a time. With the first draw, Leovold doesn't care that you are about to draw a card because it doesn't apply to you. Notion Thief sees that you are about to draw a card and replaces it with your opponent drawing the card. The opponent draws that card since (I am assuming) it is the first card the opponent would draw this turn.
3. With the second and third draw, Leovold doesn't apply initially because he only cares if your opponent would draw more than one card. Notion Thief cares and will replace your draws with your opponent drawing those cards. At this point, Leovold sees the opponent attempting to draw too many cards and then those draws (by the opponent) will be ignored.
4. The final result is your opponent drawing 1 or 0 cards depending on how many he had previously drawn that turn.
   This is entirely consistent with the rules that are cited because the draw that are being replaced are your draws, not the opponent's, and Leovold is only preventing your opponent's card draws after the replacement effect has occurred.

If you want an example of when rule 614.7 would apply, consider this scenario:
Player A controls both Notion Thief and Leovold.
Player B targets himself with Ancestral Recall.
In this circumstance, the outcome depends entirely on whether or not Player B has already drawn a card this turn. If he has, Leovold will disallow the draws off of Ancestral Recall and these draws cannot be replaced by Notion Thief. Player A will draw zero cards. If Player B has not drawn a card, the Leovold will allow the first draw, which gets replaced by Notion Thief. On the second draw, Player B still hasn't drawn a card (that card draw was replaced by Notion Thief), so the second draw is allowed by Leovold and replaced by Notion Thief. Same with the final draw with the net result being Player A drawing three cards.

@Khahan said:

@MaximumCDawg said:

Is there a general ruling or part of the Comp Rules somewhere that explains that replacement effects are replied before "can't" effects -- or vice verca?

Not that I'm aware of and that is why I'm wondering. The way the ruling is worded, a judge could reasonably state that since leovold disallows the last 2 draws of ancestral recall, the replacement effect from notion thief doesn't apply and I would get to draw 2 cards in my scenario. In plain English that is exactly what the ruling states. Like I said, I have a feeling that is not the intent and not what they had in mind with that ruling. But barring some other rule we haven't considered if a judge encountered this situation and stated that my opponent draws 1 and I draw 2 he could point to this as his justification and have the backing he needs.

Under the heading: 101. The Magic Golden Rules

101.2. When a rule or effect allows or directs something to happen, and another effect states that it can’t
happen, the “can’t” effect takes precedence.
Example: If one effect reads “You may play an additional land this turn” and another reads
“You can’t play land cards this turn,” the effect that precludes you from playing lands wins.

Edit: Didn't see the above post until after I had written. @ChubbyRain's answer is the one.