Directed probability graph - algorithm to reduce cycles?

Question

Consider a directed graph which is traversed from first node 1 to some final nodes (which have no more outgoing edges). Each edge in the graph has a probability ass

Answer 1

I found this question while researching directed cyclic graphs. The probability of reaching each of the final nodes can be calculated using absorbing Markov chains.

The video Markov Chains - Part 7 (+ parts 8 and 9) explains absorbing states in Markov chains and the math behind it.