The tension between late and early universe probes of today's expansion rate, the Hubble parameter H 0 , remains a challenge for the standard model of cosmology ΛCDM. There are many theoretical proposals to remove the tension, with work still needed on that front. However, by looking at new probes of the H 0 parameter one can get new insights that might ease the tension. Here, we argue that neutrino oscillations could be such a probe. We expand on previous work and study the full three-flavor neutrino oscillations within the ΛCDM paradigm. We show how the oscillation probabilities evolve differently with redshift for different values of H 0 and neutrino mass hierarchies. We also point out how this affects neutrino fluxes which, from their measurements at neutrino telescopes, would determine which value of H 0 is probed by this technique, thus establishing the aforementioned aim.