Basic Joint probability distribution calculation example? (X, Y) has the Joint probability distribution:
\begin{array}{|c|c|c|}
\hline
 X / Y & 1 & 2 \\ \hline
 1& \frac{1}{4}& \frac{1}{3}  \\ \hline
 2&  \frac{1}{6}& a \\ \hline
\end{array}
So $P(X=1\mid Y=1)=\frac{3}{5}$ and $P(X=2\mid Y=2)=\frac{3}{7}$.

My challenge is via calculation, how $\frac{3}{5}$ and $\frac{3}{7}$
  was calculated in this example?


$$
P(X=1|Y=1)=\frac{P(X=1, Y=1)}{P(Y=1)}= \frac{1/4}{1/6+1/4}
$$
