@oolongteasup,
Do you mean, "What is the likelihood that only 3 of those 4 players hold hands containing at least 4 cards of any suit?"
If so, it is zero. You can't deal a hand of 13 cards in 4 suits without having at least 4 cards in at least 1 suit because 4x3=12.
Otherwise, I don't know what you mean by "the one" suit.