I am trying to model a system using a continuous-time Markov chain. I want to calculate the probability that a user entering the system at a state $s$ will encounter an event $E$ (while staying in the system).
The transition probability matrix $T$ is already computed.
For some states $s$ in the state space the probability $p(E,s) = 1$.
For the rest of the states $p(E,s) = \sum \nolimits_{s'} p(E,s') T(s,s') $
Any idea of how can I solve it?