  The conductance coefficients of disordered mesoscopic devices with $n$ probes
are investigated within the noninteracting electron approximation at zero
temperature. The probes are eliminated from the theoretical description at the
expense of introducing nonlocal boundary conditions at the position of the
contacts. Conductors with a large number of weak contacts are analyzed in
detail. The ensemble-averaged conductance coefficients are in this case given
by the so-called Hauser-Feshbach formula $g_{ab} \sim p_a p_b$ where $p_a$ is
the probability for emission of an electron into lead $a$. The conductance
energy autocorrelation function is shown to deviate significantly from the
conventional Lorentzian form and to have a negative tail.
