Inside a rope of length $n$, $n-1$ points are placed with distance $1$ from each other and from the endpoints. Among these points, we choose $m-1$ points at random and cut the rope at these points to create $m$ segments.

Let $E(n,m)$ be the expected length of the second-shortest segment. For example, $E(3,2)=2$ and $E(8,3)=16/7$. Note that if multiple segments have the same shortest length the length of the second-shortest segment is defined as the same as the shortest length.

Find $E({10}^7,100)$. Give your answer rounded to $5$ decimal places behind the decimal point.