We take a uniformly random permutation of a standard deck of 52 cards, so

that each permutation has a probability of 1/52!. Define the following events:

A = \the top card is an Ace",

B = \the bottom card is the Ace of spades",

C = \the bottom card is the Queen of spades".

Determine

Pr(A | B);

and

Pr(A|C):