Markov chain simulation — inverting the cumulative row

Suppose $\{X_n,n\ge0\}$ is a Markov chain with state space $S=\{1,2,3\}$ and transition probability matrix

$$P=\begin{pmatrix}2/5&3/5&0\\3/8&5/8&0\\1/6&1/3&1/2\end{pmatrix}.$$

Suppose $X_0=3$. Then realized values of $X_1$ and $X_2$ corresponding to random numbers $0.36$ and $0.64$ respectively, from $U(0,1)$ distribution are: