Let $X$ be an infinite dimensional separable Hilbert Space with norm $||\cdot||$ and let $\mu$ be a Gaussian measure on $X$ such that $\mu(X) = 1$. What do we know about $\mu(B(0,1))$, where $B(0,1)$ is the unit ball w.r.t the norm?

This seems to me like a fundamental question but I cannot seem to find anything. Any information/references would be most appreciated.

Let $X$ be an infinite dimensional separable Hilbert Space with norm $||\cdot||$ and let $\mu$ be a Gaussian measure on $X$ such that $\mu(X) = 1$. What do we know about $\mu(B(0,1))$, where $B(0,1)$ is the unit ball w.r.t the norm?

This seems to me like a fundamental question but I cannot seem to find anything. Any information/references would be most appreciated.

EDIT: A related question which is of interest to me: Do there exist asymptotically tight bounds to $\int_{||u||> K}||u||^2 \mu(du)$?