Markov Processes and Random Walks

Hello all! I'm currently facing this problem that is giving me all kinds of fits. I'm relatively new to Markov processes, but I feel like I understand how they work. Unfortunately, figuring out the probabilities for this problem is beyond me. Can anyone lend a hand in explaining this problem? The problem: Imagine this intersection:

http://tech.metatake.com/images/3/3f/Intersection.jpg

(e.g./ Intersection #8 is only adjacent to #5 and #7) There is a policeman who moves from intersection to an ADJACENT intersection with equal probability each hour. He thinks he'll spend 1/8 of his time in each intersection. But he's wrong. Using Markov processes, explain why explicitly. * Compute T, the transition matrix * Pick a large value of n and compute T^n * Explain why he is wrong for a) Intersection #1 and #3 are considered adjacent b) Intersection #1 and #3 are not considered adjacent