Limit law of the uniform minimum

For $n\in\mathbb{N}$, let $Z_n$ be the smallest order statistic based on a random sample of size $n$ from the $U(0,1)$ distribution. Let $nZ_n\xrightarrow{d}Z$, as $n\to\infty$, for some random variable $Z$. Then $P(Z\le\ln 3)$ is equal to