[kilotaras]

  > what is the most probable distance between the two points?
  > even if they answered/guessed 1/3

1/3 is not the most probable distance, it's the expected value. The most probable distance does not exist, but PDF(d) is strictly decreasing for (d>0).

[dmillar]

You're right. Thinking back, I think I asked "what's the average distance" not "what's most probable".