Dissociation of water into H+ and OH-: Does the law of mass action hold at nanoscale?
There is definitely a breakdown of mass action at very low numbers of molecules.  This can happen either because concentrations are tiny, or because the system of interest is tiny.

In either case, your idea to turn to probability is an excellent one, and is how these systems are modeled.  But the reason doesn't necessarily have to do with quantum mechanics.  It's just a consequence that matter is not really a continuum that can have any concentration, but is in fact granular.  At the scale of atoms, there can either be an atom, or not be an atom.  You can't have 0.5 of an atom.

The right boundary at which mass action breaks down depends a bit on the particular system, in particular, if reactions are occurring that depend on H+.  In the less complicated case of no reactions depending on $\ce{H+}$, then the boundary between mass action being valid and not is actually fairly easy to calculate. If you know the average or expected value of $\ce{H+}$ ions in your water sphere (which you do, since you calculated it) the actually observed number of ions will follow a Poisson distrubtion.  If the mean number of atoms is $N$, then the standard deviation of atoms is $\sqrt{N}$, so the relative uncertainty in the mean number of atoms is proportional to $\frac{\sqrt{N}}{N}=\frac{1}{\sqrt{N}}$.  According to your calculation, $N$ is less than one, so the relative uncertainty is greater than 100%!  But if you enlarged the sphere so the expected number of ions was $N=10$, then the uncertainty would be about 32%, still pretty bad.  If you enlarged the sphere so $N=10000$, then the relative uncertainty is only 1%, meaning that mass action predictions for this system are pretty close to accurate!  Getting $N$ tht high requires a sphere about 10,000-times bigger in volume, which means the radius would have to be about 38 times bigger.  But keep in mind this result is only true for the water dissociation problem.  So each chemical system has its own scale where mass action breaks down.

For systems where reactions are occurring that depend on $\ce{H+}$, this simple logic breaks down.  Complex probabilistic simulations need to be done.  Depending on the details of the reactions, the chemical master equation or the chemical Langevin equation would have to be used. 

One time I calculated the concentration of frogs in an aquarium was about 1 zeptomolar.  I don't think we could assume frogs followed the law of mass action!