  We present exact analytical results for the differential conductance of a
finite Kitaev chain in an N-S-N configuration, where the topological
superconductor is contacted on both sides with normal leads. Our results are
obtained with the Keldysh non-equilibrium Green's functions technique, using
the full spectrum of the Kitaev chain without resorting to minimal models. A
closed formula for the linear conductance is given, and the analytical
procedure to obtain the differential conductance for the transport mediated by
higher excitations is described. The linear conductance attains the maximum
value of $e^2/h$ only for the exact zero energy states. Also the differential
conductance exhibits a complex pattern created by numerous crossings and
anticrossings in the excitation spectrum. We reveal the crossings to be
protected by the inversion symmetry, while the anticrossings result from a
pairing-induced hybridization of particle-like and hole-like solutions with the
same inversion character. Our comprehensive treatment of the Kitaev chain
allows us also to identify the contributions of both local and non-local
transmission processes to transport at arbitrary bias voltage. Local Andreev
reflection processes dominate the transport within the bulk gap and diminish
for higher excited states, but reemerge when the bias voltage probes the
avoided crossings. The non-local direct transmission is enhanced above the bulk
gap, but contributes also to the transport mediated by the topological states.

Mesoscale and Nanoscale Physics