And we can see this requirement concretely as well.

If you start in state j, the probability of being in the other states reachable from j will start increasing from 0, and the probability of remaining in state j will start decreasing from 1.

(Unless it is an absorbing state.)

Because the probabilities of being _somewhere_ will always total to 1, the sum of these derivatives must equal zero.

If you start in state j, the probability of being in the other states reachable from j will start increasing from 0, and the probability of remaining in state j will start decreasing from 1.

(Unless it is an absorbing state.)

Because the probabilities of being _somewhere_ will always total to 1, the sum of these derivatives must equal zero.