XY, XY, XY, ZZ, flop comes XYZ - odds?

[btetreau]

Hey All,

Ran into this recently in a MTT, table was full (10 heads) and I got AK, raised, and 3 callers came along. Flop was AK5, everyone went allin, and the 4 hands were AK, AK, AK, 55.

So, what are the chances that the flop will come XYZ if 3 of the 10 people hold XY and a fourth holds ZZ?

Thanks in advance.