Suppose we deal five cards from an ordinary 52 card deck. what is the conditional probability that the hand contains no pairs, given that it contains no spades?
So, there are no spades, so the probability will be out of 39. The first card being dealt can be any card of the 39, so the probability will be 39/39. The second cannot be of the same value as the first, so it will be 36/38. (suppose you drew an ace of hearts, the next card cannot be an ace of clubs or an ace of diamonds).
You will continue on, with the 3rd card drawn and the probability will be 33/37. The 4th will be 30/36. and fifth will be 27/35. Now we will multiply all these probabilities together.
You will get 39/39 * 36/38 * 33/37 * 30/36 * 27/35 = 2673/4921 or about 54% that you won’t get a pair, given that it contains no spades.