Problem - Random Pick with Weight

You have an array of positive integers representing weights. You need to pick an index randomly where the probability of picking index $i$ is proportional to its weight.

For example, if weights are $[1, 3, 2]$, then index $0$ has probability $\frac{1}{6}$, index $1$ has probability $\frac{3}{6} = \frac{1}{2}$, and index $2$ has probability $\frac{2}{6} = \frac{1}{3}$.

How can you implement this so each call runs fast, even if weights array is large?