The first thing to notice is that the path of the drunk man is the mathematical random walk with starting position $W_0 = 26$, and his position over time is a martingale. Let us denote his position after $i$ steps as $W_i$. Because his path is a martingale, it is the case that $$ E[W_i - W_0] = 0 $$ for any value of $i$. Let us denote the position corresponding to the start of the bridge (that is, at $x=0$ metres) as $W_s = 0$, and $W_e = 100$ is the position corresponding to the end of the bridge (at $x=100$ metres). The drunk man stops when he reaches $W_s$ or $W_e$ and the random walk ends. Now, suppose that we travel forward infinitely far in time, so that in all scenarios the drunk man has exited the bridge. The following must be true $$ E[W_\infty - W_0] = (W_s - W_0)P(W_\infty = W_s) + (W_e - W_0)P(W_\infty = W_e) = 0. $$ This is straightforward to solve, keeping in mind that $$ P(W_\infty = W_s) = 1 - P(W_\infty = W_e) $$ we see that the probability that the drunk man exits at the end of the bridge is $$ P(W_\infty = W_e) = \frac{26}{100}. $$