  The effect of an invasive voltage probe on the phase-coherent conduction
through a ballistic chaotic cavity is investigated by random-matrix theory. The
entire distribution P(G) of the conductance G is computed for the case that the
cavity is coupled to source and drain by two point contacts with a quantized
conductance of 2 e^2/h, both in the presence (beta = 1) and absence (beta = 2)
of time-reversal symmetry. The loss of phase-coherence induced by the voltage
probe causes a crossover from P(G) ~ G^(-1 + beta/2) to a Gaussian centered at
G = e^2/h with a beta-dependent width. ***Submitted to Physical Review B.***
