I am trying to formulate the measure of event

$E=\{B[0\infty)\cap A,B \neq \varnothing$ and $B[0\infty)\cap C= \varnothing\}$,

where $B[0\infty)$ is a Brownian path and $A,B,C$ are pairwise disjoint compact non-empty sets. I am looking for $\mu_{W}(E)$.

One guess is:

$\mu_{W}(E)=\int_{\mathbb{R}^{d}} \int_{A}