What are the Odds?
 

This happened in a hand I was in. I never saw this happen before. I thought it was bad to have more than one opponent with AA. Are you ever more likely to lose with AA and all opponents with (different) pocket pairs?
Here is the weird hand:

Ultimate Bet
No Limit Holdem Ring game
Blinds: $0.05./$0.10.
6 players
Converter

Pre-flop: (6 players) LuckyOne is Button with A[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/heart.gif[/img]
<font color="#cc0000">UTG raises to $0.35</font>, UTG+1 folds, <font color="#cc0000">CO raises all-in $3.45</font>, <font color="#cc0000">LuckyOne raises to $10.85</font>, 2 folds, <font color="#cc0000">UTG calls all-in $6.17</font>.
Uncalled bets: $4.33 returned to LuckyOne.

Flop: Q[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/club.gif[/img] ($9.89, 1 player + 2 all-in - Main pot: $10.5)


Turn: 5[img]/images/graemlins/club.gif[/img] ($9.89, 1 player + 2 all-in - Main pot: $10.5)


River: J[img]/images/graemlins/heart.gif[/img] ($9.89, 1 player + 2 all-in - Main pot: $10.5)


Results:
Final pot: $9.89
<font color="#ffffff">LuckyOne shows Ac Ah</font>
<font color="#ffffff">UTG shows Ks Kh</font>
<font color="#ffffff">CO shows Kc Kd</font>

So what are the odds of that distribution of hands pre-flop?
How many paired callers before AA no longer favorite?