One hundred random circle points in a semicircle

$100$ points are dropped independently and uniformly on a circle. The probability that some semicircle contains all of them equals $\dfrac{a}{b^c}$ with positive integers $a,b,c$ and $b$ as small as possible. Find $a+b+c$.

$201$. For $n$ points, the events 'all points lie in the clockwise semicircle starting at point $i$' are disjoint and each has probability $2^{-(n-1)}$, so the answer is $n/2^{n-1}=100/2^{99}$, and $100+2+99=201$.