Expected smallest gap among 101 uniform points

Draw $101$ points independently and uniformly from $(0,1)$. What is the expected value of the smallest distance between any two of them?

$\tfrac{1}{10200}$. All $100$ gaps between neighbouring sorted points are at least $x$ with probability $(1-100x)^{101}$ for $0\le x\le\tfrac1{100}$ (shrink each gap by $x$). Integrating this tail gives $\mathbb{E}[\text{min gap}]=\int_0^{1/100}(1-100x)^{101}dx=\tfrac{1}{100\cdot102}=\tfrac{1}{10200}$.