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 sen

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.