Close enough JtS,

The odds, with no cards seen, of drawing two Aces are 52/4 * 51/3;
i.e. one in 221
Once you see your two Kings, the remaining pack has only 50 cards, so the chance of your opponent getting two Aces is 50/4 * 49/3;
i.e. roughly one in 204

Cheers

Nigel