In Spades, I wish to know the probability a certain suit is distributed in a particular way. For example I wish to know what is the probability that the diamonds are distributed either 4-4-4-1 or 5-4-4-0 among the 4 players.
Is this question equal to the probability a hand is distributed 4-4-4-1 or 5-4-4-0 among the four suits? If this is true, then I can use the Hand pattern probabilities
EDIT: This question came up because I wanted to know what is the probability that my partner will not be able to cover my nil bid on the forth trick of a suit. Only on those two hand distributions (4-4-4-1 or 5-4-4-0) is it possible for an opponent to lead that suit, me having that suit, and my partner to not be able to cut with a spade.
I guess I need the conditional probabilities, conditioned on the number of cards I have from that suit. Do you know to find the distribution when I have either 4 or 5 diamonds?