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

E₁ : Event denotes spade is missing
$\mathrm{P}\left({\mathrm{E}}_1\right)=\frac{1}{4};\mathrm{P}\left({\overline{\mathrm{E}}}_1\right)=\frac{3}{4}$

A : Event drawn two cards are spade
$\begin{array}{l}\mathrm{P}\left(\mathrm{A}\right)=\frac{\frac{1}{4}\times \left(\frac{{ }^{12}{\mathrm{C}}_2}{{ }^{51}{\mathrm{C}}_2}\right)+\frac{3}{4}\times \left(\frac{{ }^{13}{\mathrm{C}}_2}{{ }^{51}{\mathrm{C}}_2}\right)+\frac{3}{4}\times \left(\frac{{ }^{13}{\mathrm{C}}_2}{{ }^{51}{\mathrm{C}}_2}\right)}{\frac{1}{4}\times \left(\frac{{ }^{12}{\mathrm{C}}_2}{{ }^{51}{\mathrm{C}}_2}\right)+\frac{3}{4}\times \left(\frac{{ }^{13}{\mathrm{C}}_2}{{ }^{51}{\mathrm{C}}_2}\right)}\\ =\frac{39}{50}\end{array}$