What is the probability that from a normal 52 card deck, you randomly draw a 3, and then without replacing the 3, you draw the queen of hearts?

The probability of any particular outcome is

    (number of possible successful outcomes) / (number of total possibilities)

-- On the first draw, there are 52 possible total outcomes, and
only 4 that are successful ... drawing a 3 .
The probability of drawing a 3 from a full deck is  ( 4 / 52 ).

-- On the second draw, there are 51 possible total outcomes (the first
card you drew stayed out), and only one is successful ... drawing the
queen of hearts.
The probability of this particular outcome is   ( 1 / 51 ).

-- The probability of both of them is  

                                 ( 4 / 52 ) x ( 1 / 51 ) =

                                       ( 4 / 2,652 )  =  about 0.151 percent.