[thebzax]

The question is more about what kinds of distributions are in some sense "reasonable" for this setup. A uniform distribution for wine/water is problematic because it implies a non-uniform distribution for water/wine, and it is reasonable to expect that these distributions should be the same.

The underlying problem is still underspecified, and there is a class of distributions which have the appropriate symmetry, as described in the paper. The range of possible answers is still more limited under this symmetry assumption (that the ratio of water/wine and wine/water should have same distribution) than under no assumption (in which case any probability between 0 and 1 is acceptable).