P = \left[ \begin{array}{cccc}
1/2 & 1/2 & 0 & 0 \\
0 & 0 & 1/3 & 2/3 \\
1/3 & 2/3 & 0 &0 \\
0 & 0 & 1/4 & 3/4
\end{array} \right]