It's in your stack, provided your stack isn't full. If the stack was already full then your Nosepass is gone forever.
Probopass is not a hard counter to Azumarill, it takes SE damage from water and EDIT: resists IB and PR but is vulnerable to HP if Azu happens to be carrying it. But it is looking like a very good pokemon, I'm carefully appraising every Nosepass I catch to see if I can get one with good PvP IVs.