Probability question

[Talking Poker]

No, the PAST probabilities don't change. But I promise you that it is FAR less likely that someone was dealt AA when the flop comes AAA than when the flop comes 234. Yes, when the cards were dealt, the probability for any given player to be dealt AA was 220:1. We all agree with that. But that is completely useless information to us now that we've seen the flop. When putting our opponent on a hand (why else would we care about these probabilities in the first place?), we need to use all of the information available to us, including the flop. To ignore it and think that there is still approximately a 5% chance that someone at the table is holding AA would be asinine.

I really don't get what is so difficult about this. Maybe I'm WAY OFF in my thinking here (that certainly could be the case), but this just seems like common sense to me.

I use the AA hole cards with an AAA flop because I think it is so obvious and simple to understand. A more practical application would be what I posted (and no one responded to) in this post: