The probability is the ratio of the number of queens to the total number of cards in a deck. However, when there is no replacement, you subtract 1 from the numerator and denominator.
So, for the first queen, the probability is: P = 4/52 = <em>1/13</em>
Now, for the second queen, the available cards are only 51 since 1 was already chosen. Similarly, there are only 3 queens left. Thus, the probability of getting a second queen is: P = (4/52)(3/51) = <em>1/221</em>