Which part?
If you don't understand the first statement, then just look at the definition of probability.
Let me quote from Wikipedia:
"Probability is the measure of the likeliness that an event will occur."
The key word here is measure. Measure is a non-negative value you assign
to each measurable set of your space (the assignment should have some special properties).
No measure - no probability, as simple as that, just by the mere definition.
So let me state it once again: 1) we need to agree upon which subsets of our space are measurable,
2) we need do assign them measure, and only then 3) we can ask about probabilities of different events.
Before steps 1) and 2) probability is not even defined, so questions like 3) are meaningless.
PS Your example problem with rain and plots could be easily resolved by choosing a finite number of sets
that should me measurable and assigning them proper measures. Same procedure cannot be done to solve the original problem.