A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is:

E  $\to$ Lost card not spade
A $\to$ both cards drawn are spade
$P\left(E\right)=\frac{3}{4} P\left(E^C\right)=\frac{1}{4}$

$P\left(\frac{A}{E}\right)=\frac{{ }^{13}{C}_2}{{ }^{51}{C}_2} P\left(\frac{A}{E^C}\right)=\frac{{ }^{12}{C}_2}{{ }^{52}{C}_2}$

$P\left(\frac{E}{A}\right)=\frac{P\left(E\right)P\left(\frac{A}{E}\right)}{P\left(E\right)P\left(\frac{A}{E}\right)+P\left(E^C\right).P\left(\frac{A}{E^C}\right)}=\frac{39}{50}$