  We establish a reflection principle for three lattice walkers and use this
principle to reduce the enumeration of the configurations of three vicious
walkers to that of configurations of two vicious walkers. In the combinatorial
treatment of two vicious walkers, we make connections to two-chain watermelons
and to the classical ballot problem. Precisely, the reflection principle leads
to a bijection between three walks $(L_1, L_2, L_3)$ such that $L_2$ intersects
both $L_1$ and $L_3$ and three walks $(L_1, L_2, L_3)$ such that $L_1$
intersects $L_3$. Hence we find a combinatorial interpretation of the formula
for the generating function for the number of configurations of three vicious
walkers, originally derived by Bousquet-M\'elou by using the kernel method, and
independently by Gessel by using tableaux and symmetric functions.
