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 $\mu_{W}(E)$. Any ideas?

One guess is:

$\mu_{W}(E)=\int_{t_{1}}^{\infty}\int_{0}^{\infty} \int_{B} \int_{A} \int_{\mathbb{R}^{d}}p(x_{1},x_{2},t_{1})p(x_{2},x_{3},t_{2}) dx_{1}dx_{2}dx_{3}dt_{1}dt_{2}+ $

$+\int_{t_{1}}^{\infty}\int_{0}^{\infty} \int_{A} \int_{B} \int_{\mathbb{R}^{d}}p(x_{1},x_{2},t_{1})p(x_{2},x_{3},t_{2}) dx_{1}dx_{2}dx_{3}dt_{1}dt_{2}-$

$-\int_{0}^{\infty}\int_{C} \int_{\mathbb{R}^{d}} p(x_{1},x_{2},t_{1}) dx_{1}dx_{2}dt_{1}$