minimum random variable subscript expectation

Suppose there are $n$ R.V. $X_1,...,X_n$ drawn from $U(0,1)$. Define $$Z_{i}=\frac{X_{(i)}}i$$, where $X_{(i)}$ is the $i$-th minimum value among $X_1,...,X_n$. What is the expected index of the minimum $Z_{i}$, i.e., $$E(i|Z_{i}=\min(Z_1,...,Z_n))$$