hang on! Not sure but I think I might have got it!
I think wasn't thinking clearly about the definition of "fractile" but, if I am now thinking about this right, the answer is, for my 3 bar example (my first example ), the vertical line should cut straight in the middle of the v=1 bar so that the cumulative probability of the 0.5 fractile is simply 1/2.
And, for my 4 bar example (my second example ), the vertical line should go exactly between the v=1 bar and the v=2 bar so that the cumulative probability of the 0.5 fractile is also simply 1/2.
More generally, and only if I am thinking about it completely correctly now, EVEN always for a discrete random variable;
The cumulative probability of n-fractile ( 0 <= n <= 1 ) is simply n.
But, because this is critical to the research I am currently doing, I MUST make absolutely sure I understood that correctly before moving on.
Have I now got that exactly right?