  Measuring flux ratios of ultra-high energy neutrinos is an alternative method
to determine the neutrino mixing angles and the CP phase delta. We conduct a
systematic analysis of the neutrino mixing probabilities and of various flux
ratios measurable at neutrino telescopes. The considered cases are neutrinos
from pion, neutron and muon-damped sources. Explicit formulae in case of mu-tau
symmetry and its special case tri-bimaximal mixing are obtained, and the
leading corrections due to non-zero theta_{13} and non-maximal theta_{23} are
given. The first order correction is universal as it appears in basically all
ratios. We study in detail its dependence on theta_{13}, theta_{23} and the CP
phase, finding that the dependence on theta_{23} is strongest. The flavor
compositions for the considered neutrino sources are evaluated in terms of this
correction. A measurement of a flux ratio is a clean measurement of the
universal correction (and therefore of theta_{13}, theta_{23} and delta) if the
zeroth order ratio does not depend on theta_{12}. This favors pion sources over
the other cases, which in turn are good candidates to probe theta_{12}. The
only situations in which the universal correction does not appear are certain
ratios in case of a neutron and muon-damped source, which depend mainly on
theta_{12} and receive only quadratic corrections from the other parameters. We
further show that there are only two independent neutrino oscillation
probabilities, give the allowed ranges of the considered flux ratios and of all
probabilities, and show that none of the latter can be zero or one.
