Given a segment of length $$$1$$$, randomly pick two points $$$A$$$ and $$$B$$$ (we can assume that $$$A$$$ is to the left of $$$B$$$, if not, just swap them), what is the expected length of segment $$$AB$$$.

For Chinese readers, Chinese statement is here:

Someone says that it is related to the theoretical proof of Chtholly Tree, but I simply cannot understand why...