find the probability of a spade from a five-card deck I am trying to solve a simple exercise from a probability book but I have no idea how. Given a five-card deck containing: ace of spades, king of spades, king of hearts, queen of spades, and queen of hearts, there are 2 players and each one has exactly one card. You observe evidence that one player has a picture card (king or queen). What’s the probability that the other player has a spade? I think at conditional probabilities, but I don't know how to model this events. P(A|B) where A is the event of extracting a spade and B represents event of having a spade from a picture card. I know that if I observe picture card than the probability of being a spade is 1/2.

_Hint_

Taking your "All that I know..." means that a random card "opened" is seen to be a face card,

either it is a spade face card (Pr = ?) in which case the other card has a Pr of $\frac14$ of being a spade,

or it is a non-spade face card (Pr = ?) in which case the other card has Pr of $\frac24$ of being a spade

Can you now frame it in terms of conditional probabilities, and apply the law of total probability ?