This is a Markov chain {Xn, n >= 0} with state space E = {1,2,3} The transition matrix P is

.2 .5 .3

.2 0 .8

.3 .1 .6

The initial distribution vector is p(0) = (0,1,0).

How do I calculate these?

Pr{X3 = 3 given that X1 = 1}

Pr{X3 in {2,3} given that X1 = 1}

Pr{X2 = 1, X3 = 2}