Is this probability distribution data structure already discovered?
This is a straightforward use of augmented data structures.  I wouldn't expect it to be publishable on its own; it's more of an undergraduate exercise.  So, I would expect that it's probably been thought of many times before by many people independently, but not necessarily written down in any particular research paper.

The idea of storing in the node of a tree the number of leaves under it is a completely standard idea in augmented data structures.  So too is the idea of storing each node the sum of the values in the leaves under it.  If you read some algorithms and data structures textbooks that describe augmented data structures, I'm sure you'll find examples of both of those motifs.