prob. of pocket aces against pocket kings heads up

[findingneema]

No. The probabilities are not independent, since you remove cards from the deck. In the exact heads up situation, one player gets AA (or KK, doesn't really matter) 6/1326. The other player gets the other hand 6/1225 (see how many fewer hands are possible once two cards are removed?). Because player A could get AA or KK, you have to double it. So,

(6/1326) * (6/1225) * 2 = 0.0000443 = 0.00443%
or ~ 22,559 to 1

i.e., for every 22,560 hands, you will expect one AA vs KK matchup. Same for any particular pp vs any other pp.

Now, of course if you already have KK, the odds of the other guy getting AA is exactly 6/1225 or ~ 203 to 1.