What is the probability there is no prime between $n$ and $n+\ln(n)$?

Consequences of the Prime Number Theorem tell us the probability of $n$ being prime is $1/\ln(n)$. This also means that the number of expected primes between $n$ and $n+\ln(n)$ is close to $1$, but not always. What is the probability there is no prime between $n$ and $n+\ln(n)$?

from Hot Weekly Questions - Mathematics Stack Exchange