A man hikes up a mountain, and starts hiking at 2:00 in the afternoon on a Friday. He does not hike at the same speed (a constant rate), and stops every once in a while to look at the view. He reaches the top in 4 hours. After spending the night at the top, he leaves the next day on the same trail at 2:00 in the afternoon. Coming down, he doesn't hike at a constant rate, and stops every once in a while to look at the view. It takes him 3 hours to get down the mountain.

Q: What is the probability that there exists a point along the trail that the hiker was at on the same time Friday as Saturday?

You can assume that the hiker never backtracked.