the likelihood of opponents hand containing singletons is totally independent of the circumstance of you having a singleton...
the other hands may be (more) distributional by virtue of yours being so ( in the sense that there are more cards in the suit(s) that you are short in and less cards in the one(s) you are long in)
but the probabililty of them having singletons still abides by the same probabilities (with regards to the number of cards available in a suit to be divided between remaining hands)
of course if you got
AKQxxxxxxxx
x
-
x
naturally at least two hands have a singleton or void in the spade suit....
but how the remaining 39 cards, and especially for this argument, 37 cards in the non-spade suits, are distrtibuted RANDOMLY in the other hands makes all card permutations EQUALLY LIKELY and thus follow the same principles as when we are talking about the frequency distributions of the suit-cards in 4 hands...only thing that has changed is the number of hands and the number of cards..
in other words...the probability of balanced hands is more likely than unbalanced hands

Help
