Four isolated mountain villages named Albera, Berna, Civa and Dazio are connected by six roads, so there is a direct route between every pair of villages. There are no other roads to the outside world.

To entertain themselves, the mountain trolls decide to block three of these roads. If the trolls pick the three roads to block at random, what is the probability that one of the villages ends up completely cut off from the other three villages?