While reading a paper, I see the reflection principle is $$ Pr(X(t)\le x, M(t)>y)=Pr(X(t)\le x-2y), \ \ y\ge \max{(x,0)}, $$ where $X(t)=\sigma W(t)$, $W(t)$ is a standard Brownian motion, and $M(t)$ is the running maximum of $X(t)$. This is the reflection principle with drift $\mu$ equal to $0$. However, this paper briefly states that by changing the probability measure, the reflection principle can be generalized as $$ Pr(X(t)\le x, M(t)>y)=e^{y\mu/D}Pr(X(t)\le x-2y), \ \ y\ge \max{(x,0)} $$ where drift $\mu$ is an arbitrary constant, $D=\frac{1}{2}\sigma^2$. Now, $X(t)=\mu t+\sigma W(t)$ is a drifted Brownian motion, and $M(t)$ I believe is the new process generated by drifted Brownian motion.
The thing is that I don't have enough background on measure theory, I've tried my best only to find nothing. Can anybody do me a favor? I would appreciate any help from you.