Let I1:=(0,1), I2=(a,a+1), where a≥1, be open intervals of R. Let M:=I1∪I2. Choose f:M→R,x↦{0if x∈I11if x∈I2
f is continuous. Choose the metric to be the standard Euclidean one. Choose μ to be the one-dimensional Lebesgue-measure (i.e. dμ=dx).
In this case, the r.h.s. of your equation will be equal to 1. Your l.h.s. refers to a single sample trajectory of the Wiener-process. If this trajectory, considered as a trajectory in R, starts in I1, it cannot enter I2. So the l.h.s. will be equal to 0.