Let $\left(\, B_{t}\,\right)_{t\ \geq\ 0}$ be a Brownian motion. Calculate the probability of the event: $$ E\equiv\left\{\,\exists\ \epsilon > 0 : \forall\ 0 < h < \epsilon, \max_{t\ \in\ \left[\, 0,h\,\right]}B_{t} > \left\vert\,\min_{t\ \in\ \left[\, 0,h\,\right]}{B_t}\right\vert\,\right\} $$
Now, I assume that we can apply reflection principle to calculate supremum of the brownian motion, however, I have no idea how to actually approach the problem. Any advice on how to get to the solution is highly welcome.