what are the odds of one opponent [fullt table] having AA, when you are holding AQ and there is an Ace on the flop??

busted out late in a MTT on this... I know the chances of u getting AA is like 1/220.
but the probability of an opponent having it when two of the aces are known to you....
does it just drop it in half? to 1/440? or is it more complicated than that??

my brain is shutting down for the night...

thanks to any help here.

There are 5 known cards, the 3 on the flop and the 2 in your hand. That leaves 47 cards remaining in the deck so there are 47*46 = 2162 2 card combinations. There are 2 possible aces he can be dealt on his first card and 1 Ace he can be dealt for his second card; so out of those 2162 combinations only 2 of them result in him holding pocket Aces. The odds of then should be (providing my logic is correct)

2 in 2162 = 1 in 1081

Arx