In a forest area of Northern Europe there may be wild lynx. At a particular time the number $X$ of lynx can be between 0 and 5 with  

$$
\operatorname*{Pr}(X=x)={\left(\begin{array}{l}{5}\\ {x}\end{array}\right)}\,0.6^{x}0.4^{5-x}\quad(x=0,\ldots,5).
$$  

A survey is made but the lynx is difficult to spot and, given that the number present is $x$ ,the number $Y$ observed has a probability distribution with  

$$
\operatorname*{Pr}(Y=y\mid X=x)=\left\{\begin{array}{l l}{{\left(\begin{array}{l}{{x}}\\ {{y}}\end{array}\right)0.3^{y}0.7^{x-y}}}&{{(0\leq y\leq x)}}\\ {{0}}&{{(x<y)}}\end{array}\right..
$$  

Find the conditional probability distribution of $X$ given that $Y=2$ .  

(That is, find $\operatorname*{Pr}(X=0\mid Y=2),\ldots,\operatorname*{Pr}(X=5\mid Y=2))$