  We develop a microscopic theory for the point-contact conductance between a
metalic electrode and a strongly correlated material using the non-equilibrium
Schwinger-Kadanoff-Baym-Keldysh formalism. We explicitly show that in the
classical limit, contact size shorter than the scattering length of the system,
the microscopic model can be reduced to an effective model with transfer matrix
elements that conserve in-plane momentum. We find that the conductance $dI/dV$
is proportional to the {\it effective density of states}, that is, the
integrated single-particle spectral function $A(\omega=eV)$ over the whole
Brillouin zone. From this conclusion, we are able to establish the conditions
under which a non-Fermi liquid metal exhibits a zero-bias peak in the
conductance. This finding is discussed in the context of recent point-contact
spectroscopy on the iron pnictides and chalcogenides which has exhibited a
zero-bias conductance peak.
