Five cards are independently and randomly picked from a standard 52 card deck and each card is recorded in sequence. Each card that is picked is then put back in the deck, so it is possible to record the same card more than once. Determine the probabilities of the following events:
a. all cards are different
b. at least two of the cards have the same value
c. at least two of the cards have the same value, given that the first card drawn is an ace
d. at least three cards have the same value, given that at least two of the cards have the same value