An edge that connects more than two nodes in a graph?
When edges connect more than two nodes, you don't have a graph, you have a hypergraph. More precisely, since transitions are oriented (you're starting from a digraph) and there are probability on each transition, you have a weighted hyperdigraph. I'm not sure having this term will help you that much: as data structures go, this isn't that much of a classic.

Transitions with multiple origins rather remind me of Petri nets. If your probabilities are rational numbers and there are no loops, you can scale them to integers. Otherwise you would need to reach for probabilistic Petri nets, I think.