Suppose every point has the same probability, then this probability may not be different than zero. We cannot have a distribution function in the same way we do for discrete random variables.

This does not mean that the probability of every event has to be zero.

For instance the probability of the first
half circle has to be 1/2,
that of a quarter circle is 1/4,
a segment
[*b*,*c*] will have probability *c*-*b*.