Question 1: Let $W_t$ be a Brownian motion. Then how could we prove that $$\Pr\left\{\sup_t|W_t|<b\right\}=1-\frac{4}{\pi}\sum_{j=1}^\infty \frac{(-1)^j}{2j+1} \exp\left\{-\frac{\pi^2(2j+1)^2}{8b^2}\right\}.$$
Question 2: Let $B_t$ be a Brownian Bridge. Then how could we prove that $$\Pr\left\{\sup_t|B_t|<b\right\}=1+2\sum_{j=1}^\infty (-1)^j \exp\left\{-2j^2b^2\right\}.$$
I appreciate any hint!
For question 2: I worked on the distribution of a standard Brownian motions, $W_t$, with $W_1=0$. No success so far.