A man starts at the point O on the map below. He chooses a path at random and follows it to point B1, B2, or B3. From that point, he chooses a new path at random and follows it to one of the points A1 – A7. Suppose the man arrives at point A4, but it is not known which route he took, what is the probability that he passed through each of the three points: B1, B2, B3? Calculate each one.