Interesting. This terminology really makes no sense without more shared context, in my view. For example, I would not describe something that happens to me every month as a "remote possibility". Yet for a 3% chance event, repeated every day, monthly occurrences are what we expect. Similarly, someone who describes events as "nearly certain" would surely be embarrassed when one of the first 20 fails to happen, no?
I'm not only talking about repeated events, though. If someone told me about 20 different events that they were almost certain, and one failed to happen, I would doubt their calibration.
The terms aren’t causing this confusion, it’s that you’re applying them to less specific subjects, in particular omitting periods. “3% chance per day” makes sense, “remote chance on any particular day” makes sense, “remote chance” does not make sense, “3% chance” does not make sense. You’d also need to say “nearly certain over any 30 day period”, though if the odds are 3%/day then it’s only (just into) probable, not nearly certain—60%. It’d have to be 10%/day (not a remote chance, but highly improbable) to be nearly certain (96%) over 30 days.
If something happens to you every month, that's a certainty. If it has a 3% chance to happen to you on any given day, its a remote possibility that it will happen to you on any given day