Simple Probability of Playing Cards

Question

An ordinary deck of playing cards has four suits: hearts, spades, diamonds, and clubs. Suppose you have a reduced deck of eight playing cards, consisting of four aces and four kings. I draw two cards from the deck and look at them without showing you. I then tell you that at least one of my two cards is an ace. If you use Bayes’ rule, what probability should you now assign to the claim that both of the cards I drew are aces? Suppose I told you that one of my cards was the ace of hearts. If you use Bayes’ rule, what is the probability that both of the cards I drew are aces?