Here's a link to the 1981-2010 "normal" values for Cork.
In that, you will find line entries giving the number of days that record small, medium and medium-large amounts of rainfall. You could assume the first set would not affect cyclists much at all, so would say the second and third lines tell the story on percentage of time it might rain, I would say for a month where there are entries of 8 and 4 days in those, you could say 25% of hours for the 8 days and 50% for the 4 days. Both of those add up to 2 days, so a total of 4 days out of 30 or 31.
So in summary, the answer is probably around 10 to 15 per cent chance of significant rain falling in any given hour. That would be in the wetter months (October to April basically) so probably 5 to 10 per cent chance in the late spring and summer.
Of course I don't have to tell you rainfall can be feast or famine, some months are going to be a lot wetter than average and some a lot drier so those are only long-term averages. You could get a soaker several times in a week in a bad spell and you could go two or three weeks without seeing any rain at all.