Cards are drawn one by one in a pack of well shuffled cards replacement until all the cards are drawn then

Let us make a sample space of 52 dimensions (i.e.) each point of sample in an ordered point of the form {x₁, x₂ ..... x₅₂}
Total number of sample poins are 52!
Sample point on which x₁₃ is spade is  ${13}_{C_1}\times 5!$

Probability of getting spade on
${\mathrm{x}}_{13}=\frac{{13}_{{\mathrm{C}}_1}\times 51!}{52!}=\frac{1}{4}$
Similarly number of sample points on x₅₂ is spade
$={12}_{{\mathrm{C}}_1}\times 51!$
Number of sample points having king at x5 and queen
at x₁₀ will be $4_{{\mathrm{C}}_1}\times 50!$ 
Required probability  $=\frac{16\times 50!}{52!}=\frac{4}{663}$