  We consider sections of the \'etale homotopy exact sequence of a hyperbolic
curve over a number field. We prove that two sections whose restrictions to
decomposition groups are conjugate on a set of valuations of density one are
globally conjugate, which establishes the local-global principle for the
conjugacy classes of sections. In fact, we obtain this result as a corollary of
a more general property concerning sections of the \'etale homotopy exact
sequence, so-called finite covering property, which we prove as our main
result.
