  We derive the asymptotic behavior of hitting probability at small target of
size $O(\epsilon)$ for reflected Brownian motion in domains with suitable
smooth boundary conditions, where the boundary of domain contains both
reflecting part, absorbing part and target. In this case the domain could be
localized near the target and explicit computations are possible. The
asymptotic behavior is only related to $\epsilon$ up to some multiplicative
constants that depends on the domain and boundary conditions.
