  We consider N vicious walkers moving in one dimension in a one-body potential
v(x). Using the backward Fokker-Planck equation we derive exact results for the
asymptotic form of the survival probability Q(x,t) of vicious walkers initially
located at (x_1,...,x_N) = x, when v(x) is an arbitrary attractive potential.
Explicit results are given for a square-well potential with absorbing or
reflecting boundary conditions at the walls, and for a harmonic potential with
an absorbing or reflecting boundary at the origin and the walkers starting on
the positive half line. By mapping the problem of N vicious walkers in zero
potential onto the harmonic potential problem, we rederive the results of
Fisher [J. Stat. Phys. 34, 667 (1984)] and Krattenthaler et al. [J. Phys. A
33}, 8835 (2000)] respectively for vicious walkers on an infinite line and on a
semi-infinite line with an absorbing wall at the origin. This mapping also
gives a new result for vicious walkers on a semi-infinite line with a
reflecting boundary at the origin: Q(x,t) \sim t^{-N(N-1)/2}.
