Holdem - Flop problem

[MarkD]

Given that you have AJo (let’s say AsJc) and the flop comes Kxx, how do I calculate the probability that my opponent(s) has a king? (I realize that this will be weighted by my read, but I don’t want to worry about that atm).

I am looking for the method, not just the result. In fact I care less about the result than I do about the method used to solve the problem.

Case 1: 1 opponent
Case 2: 2 opponents
Case 3: 3 opponents

I assume the answers are:
Case 1:
1-C(44,2)/C(47,2)

Case 2:
1-C(44,4)/C(47,4)

Case 3:
1-C(44,6)/C(47,6)

But this seems almost too simple so I think it’s wrong.