Cameron-Martin theorem for a linear drift

For the Cameron-Martin space of Wiener measure path $h(s)=\mu s$, the Cameron-Martin theorem says that translation of Brownian motion by this linear function changes its law through time $t$ by the density

For ${\tau }_{a,b}=\inf \{t\ge 0:B_t+bt=a\}$ with $a,b>0$,The Cameron-Martin likelihood at a driftless path hitting $a$ at time $t$ is $e^{ab-b^{2}t/2}$.