Communications in a computer network can be described by a network G $=($V$,$ E$,$ w$)$ where the edge weights $0<=$ w$($u$,$ v$)<=1$ represent how secure communications between nodes u and v are $(0$ indicates that they always fail and $1$ that they are completely secure$).$ We can interpret w$($u$,$ v$)$ as the probability that a packet sent from u to v will successfully reach v$,$ and we can further assume that these probabilities are independent.

How can Dijkstra's algorithm for the shortest path be used to find the maximum probability of a packet reaching all other nodes in the network by defining new weights w$$ from w$?$ Note that you are not supposed to modify the Dijkstra algorithm itself. Hint: How can multiplication be turned into addition?