Probability of going from node a to node b in an undirected graph. I have a graph with n nodes. Each of which represents an activity (play, walk, sleep, etc). If I'm standing at node 1 (any), what is the probability of going from 1 to j (another node) if probability is a number between 0 and 1 (closed) between 2 nodes that refers to the chance of going in exactly one step from one to the other. And in general the probability of going from i to j is the multiplication of the probability of the nodes involved in the transition.
I was thinking about using Dijkstra's algorithm to calculate the shortest path taking into account that by shortest I mean taking the higher probability edge from the successors of the actual node and avoiding the edges with 0 values.
What would you recommend me to do ?

Your question seems to be a bit ill-posed (it's not really clear what question you're trying to answer), but what you've got here is a Markov chain, and there are standard techniques for answering questions about them.
