I don't know what does it mean to "require probability".
I'd say that it "is probability". The concept that is in our heads, mind you.
When you are guessing between the exhaustive and mutually exclusive outcomes A, B and C in such a way that
guess(A)>0, guess(B)>0, guess(C)>0
and
guess(A or B or C) = guess(A) + guess(B) + guess(C) = 1
and
guess(A or B) = guess(A) + guess(B), guess(A or C) = guess(A) + guess(C), guess(B or C) = guess(B) + guess(C)
then
guess is a probability measure as defined by Kolmogorov, for example.
That's why most people don't see any problem in calling that "probability".
You may like the name of "guessing" better but insisting in that it should not be referred to as probability and it doesn't require probability seems an uphill battle.