A card is picked up at random from 52 playing cards. Given that the picked card is a queen, then the probability of this card to be a card of spade is :

$\frac{1}{4}$

No. of spade cards = 13

given the spade card is parked 

no. of ways of pick queen = ${ }^{13} C_1$ = 13

No ways of picking one card from deck = ${ }^{52} C_1$ = 52

so probability = $\frac{13}{52} = \frac{1}{4}$