let's play this hot/cold where it's heads up, AK vs 22, and both players know what the other has

there are 6 cards in the deck which improve AK:

So you have 6 chances on each draw of the card out of the deck for an A or K to be picked, thus you end up with:

(6/48)(6/47)(6/46)(6/45)(6/44)

Now, there are 2 cards which improve 22, so on each draw there is are 2 chances for a 2 to come out:

(2/48)(2/47)(2/46)(2/45)(2/44)

There are some other long-shot ways for AK to win:

Board includes QJT,
board has 2 pair, both of which are higher rank than 2
board has full house with cards higher rank than 2
board has 4 of a kind
board has a 4 flush with the suit of either the A or K

All of these are remote possibilities.

This should get you started. The rest is just calculus.