It depends on who holds what, and what action is taken.
If I am holding the QQ, and I fold, or if I am holding the KQ and I bet, then the probability of the Q hitting on any further street is 1 (rounded off to the nearest 3 decimal places).
Since there are 3 cards on the flop the probability of the Q hitting is 3/5
QED
If the situations are reversed, then the probability is the limit approaching 0.
If the K in the KQ hand is taken into account, then according to string theory, on being dealt a K along with any other broadway card, the other 3 kings disappear from the deck unless two of them are in an opponents hand.
String theory applies because every card is attached to a cosmic string, which pulls them from the deck as necessary.
I hope this clears things up.