This is how I thought about this problem, but I am not completely sure it is right:
There are four Queens so the number of arrangements of the Queens = 4!
There are 52! possible combinations of all the cards.
There are (52-4)! = 48! combinations for all the cards without the Queens.
Then the probability of the four Queens occurring consecutively would = (4!48!)/52!
Is this logic alright?