As to the mathematical question, there are 3 each of 99 and 77. I consider 77 the most likely after this betting sequence, but we're abstracting from that.

On the Q hands: Let's say all-in has QJ+ and caller, if he has a Q, has KQ+. There are 2 Qs in the deck, 2 Ks and 4 aces. Moreover, 60% of the time, all-in has KQ or AQ. So, there are 4+8-.6= 11.4 of those hands.

So, if he'll play KQ or AQ this way (which I consider strange with the PF limp-call) as often as he will 99 or 77, then he has KQ or AQ almost twice as often as the set.

I wouldve bet alot more than the money available in this pot that UTG had a set so i folded.

BB had QJ and UTG had AQs.....UGH!!!

I still think the fold was good in general. I was almost certain the the BB has a KQ type hand but never imagined that UTG would have AQ. I mean not too many people limp AQs UTG in 6 max, but even if he did, I wouldve thought he wouldve raised all in. Why not? Hes not going to fold if I shove in ..or if anyone elses does after me, so he might as well not give anyone odds to catch a straight and lose what will be a pretty big pot on the turn.

Meh, maybe it was a bad fold. The pot is BIG....but this just looks like a set to me like 90% of the time.