Zeno's Fifth Paradox

Do events of probability 0 ever occur?  This might be called "Zeno's 
Fifth Paradox", since it so closely resembles the four most famous of
Zeno's paradoxes of motion and change.  It's most similar to "The 
Arrow", i.e., before an arrow can reach the target it must reach 
the half-way point...etc, thus motion is impossible. Similarly we 
could imagine Zeno arguing that the probability of the arrow landing 
in a certain region of the target is equal to the ratio of that 
region's area to the total target area.  As the region gets smaller 
the probability gets less, and there is zero probability of the 
arrow's point landing on any particular point of target.  Thus, 
the arrow can't possibly hit the target.

As with Zeno's other paradoxes, this one is easy to resolve from a 
strictly mathematical standpoint, where we are free to *define* 
concepts of limits and measure, but not so easy from the standpoint 
of physics, i.e., does the world really work that way?  (See the
note on Zeno's Paradox of Motion.)  For example, Zeno's "Stadium" 
paradox was really about special relativity (not bad for 300 B.C!), 
and our "Target" paradox could be regarded as an argument for the 
fundamental quantum character of nature, and the uncertainty principle. 
Maybe if Plank's constant was *zero* it really *would* be impossible 
to hit the target.  Has anyone ever produced a consistent version of 
the laws of physics with h=0?