But how do you arrive at them? Intuition doesn't deal with 0.01 and 0.00001. Intuition deals with vague notions of likely and unlikely, which also change depends on what you ate for lunch and the phase of the moon.

I think there are plenty of cases where I can give you a intuitive answer that won't change from 0.01 to 0.00001 depending on what I ate for lunch.

The chance that I die in the next year is higher than 0.00001 but lower than 0.01.

If you don't have an intuition that allows you to do so, I think it's because you don't have enough exposure to people making distinctions between 0.01 and 0.00001.