"with probability 1" is a fairly standard phrasing that is equivalent to infinitesimally-small probability (e.g., a more precise statement might be: the set of

"with probability 1" is a fairly standard phrasing that is equivalent to infinitesimally-small probability (e.g., a more precise statement might be: the set of oracles where the result is not true has "zero Lebesgue measure" -- I haven't checked to see exactly what formal statement they use).