Problem - Random Pick Index

Given an integer array with possible duplicates, you need to randomly return an index of a given target value. Each occurrence must have equal probability of being chosen.

For example, if the array is $[1, 2, 3, 3, 3]$ and target is $3$, you should return index $2$, $3$, or $4$ with equal probability $\frac{1}{3}$ each.

The challenge: the array is given once in the constructor. How can you pick fairly without preprocessing all target values?