A Markov chain on state space {1,2,3,4,5,6} has transition matrix

$\displaystyle
\begin{pmatrix}
0 & 0.5 & 0.25 & 0.25 & 0 & 0\\
0.25 & 0 & 0 & 0.25 & 0.50 & 0\\
0 & 0 & 1 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 1 & 0\\
0 & 0 & 0 & 0.40 & 0.40 & 0.20\\
0 & 0 & 0 & 0 & 0 & 1\\
\end{pmatrix}
$

Calculate $\displaystyle P(X_3\neq5|X_1=5$ I am not sure how to do this and I think something similiar is likely to appear on the final exam tomorrow so please help me out..
Are the following correct?
$\displaystyle P(X_2=5|X_1=2)=p_{25}=0.50$
$\displaystyle P(X_3=5|X_1=2)=p_{25}p_{55}+p_{24}p_{45}=0.45$
$\displaystyle P(X_3=2|X_1=5)=0$