Hello, I have two problems I'm stuck on. Any hints would be appreciated.

$\displaystyle \{X_n : n\geq0\} \mbox{ is a Markov Chain and suppose } P_{ii} > 0 $

$\displaystyle \eta_i \mbox{ is the exit time from state i}$

$\displaystyle \eta_i = min\{n \geq 1 : X_n \neq i\}$

How would I derive the distribution of $\displaystyle \eta_i$?

Secondly, suppose that whether not a team wins the Super Bowl depends on the number of Super Bowl wins for that team in the last three seasons. How would I transform this into a Markov Chain? I'm having trouble identifying the state space. Thank you.