We report low-temperature measurements of current-voltage characteristics for highly conductive Nb/Al-AlOx-Nb junctions with thicknesses of the Al interlayer ranging from 40 to 150 nm and ultra-thin barriers formed by diffusive oxidation of the Al surface. In the superconducting state these devices have revealed a strong subgap current leakage. Analyzing Cooper-pair and quasiparticle currents across the devices, we conclude that the strong suppression of the subgap resistance comparing with conventional tunnel junctions originates from a universal bimodal distribution of transparencies across the Al-oxide barrier proposed earlier by Schep and Bauer. We suggest a simple physical explanation of its source in the nanometer-thick oxide films relating it to strong local barrier-height fluctuations which are generated by oxygen vacancies in thin aluminum oxide tunnel barriers formed by thermal oxidation.
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