Consider that we are comparing the properties of two independent and identically distributed random variables, $W_1 - W_0$ and $W_2 - W_1$. If $W_1 > 0$, then two conditions must be satisfied to get $W_2 < 0$.
$$
$$
Firstly, the absolute size of $W_2 - W_1$ must be greater than $W_1 - W_0$. By symmetry, this occurs with probability $\frac{1}{2}$. Secondly, the sign of $W_2 - W_1$ must be negative, which also occurs with probability $\frac{1}{2}$. Therefore, we get
$$
P(W_2 < 0 | W_1 > 0) = \frac{1}{4}.
$$