An intelligence service has $12$ agents in an enemy country. In the graph below, each node i represents an agent, and an arc $($i$,$ j$)$ implies that i and j can communicate with each other. If i and j communicate, the message passed between them might be intercepted with a probability pij, as indicated on the graph. The group leader wants to transmit a confidential message to all the agents while minimizing the total probability that the message is intercepted. Explain how this problem can be solved as a minimum weight spanning tree problem and find the resulting probability of interception.