Consider a sentence
Scotland can be very warm in September.
Here, does it mean that Scotland will surely be very warm in September or does it mean that Scotland may or may not be very warm in September?
Uncertainty is a poor term to describe what can expresses.
It's true that can implies a kind of "uncertainty" about any future eventuality; it takes for granted that the future is inherently unknowable and cannot be predicted. But can doesn't address certainty: it is concerned with possibility. It asserts quite confidently that a hypothetical eventuality is not impossible.
In many cases can implies that the eventuality has occurred in the past:
John can bench-press 400 pounds. (I've seen him do it).
Scotland can be quite warm in September. (When I was there in '05 it occasionally hit 80 degrees).
In other cases can expresses contingent possibility:
If you study diligently you can pass this test.
Can stops short of predicting that a future eventuality will occur, but it emphatically denies the validity of any assertion that the eventuality cannot occur.
In your context applies the definition #2 a. from the American Heritage® Dictionary of the English Language:
can
2 a. Used to indicate a possibility or probability: I wonder if my long lost neighbor can still be alive. Such things can and do happen.
This said, it means that Scotland may or may not be very warm in September, so the potential exists but we don't know for sure what is going to happen.
I don't know what you mean by "definite possibility" so I'll address the questions you ask about your sentence.
Consider a sentence
Scotland can be very warm in September.
Here, does it mean that Scotland will surely be very warm in September
No, it does not mean this.
For this you can use is
Scotland is very warm in September.
There is no "possibility" expressed in this sentence, only a fact.
You could also use
Scotland will be very warm in September.
Like any statement about the future, this is a prediction. But this prediction is so strong that it is stated as a fact. That is, the person saying this sentence is predicting with 100% assurance that in September Scotland is very warm.
or does it mean that Scotland may or may not be very warm in September?
What it means is this:
It is possible for Scotland to be very warm in September.
It is not saying it will be. But it is a counter statement to the assertion that It is not possible for Scotland to be very warm in September. That is, your sentence rejects this idea. Perhaps this is what you mean by "definite possibility", for one can rewrite my above sentence as
It is definitely possible for Scotland to be very warm in September. (And whoever says that this is impossible is wrong.)
Whether Scotland will be very warm in any given September is not predicted, just the assertion that it is possible to be.
Thus, by implication, it does mean
Scotland may or may not be very warm in September
so bring some warm weather clothes to wear just in case Scotland is very warm if/when you go there in September.
Based on LDOCE, sense 9, can can be used to say what sometimes happens or how someone sometimes behaves as in
It can be quite cold here at night.
Peter can be really annoying.
It's true, based on LDOCE sense 4, that can also can be used to say that something is possible as in
There can be no doubt that he is guilty.
The boxes can be stored flat.
Can he still be alive after all this time?
It's a distinct possibility.
Scotland can be very warm in September.
Offhand, I'd say at least once in seven years, possibly more often. The opposite would be:
Scotland is hardly ever warm in September.
Meaning, less often than once in seven years.