AA KK AK what are the chances

[PaultheS]

One opponent, given that you have AK, has:

C(3,2) + C(3,2) = 3 + 3 = 6 ways to get AA or KK out of C(50,2) = 1225 possible hands. So, the probability he has AA or KK is 6/1225 = 0.004898.

With no other information, the probability he has AA or KK is (C(4,2) + C(4,2)) / C(52,2) = 0.009050.

So, the fact that you have AK decreases the chances he has AA or KK from 0.9050% to 0.4898%.