So we know that if given two finite vector spaces $V,W$ then the $\dim(V\cup W)=\dim(V)+\dim(W)-\dim(V\cap W)$ This curiously corresponds with the Probability formula of, given two probabilities $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Question, is this a mere coincidence or is there something deeper going on? Probabilities are always numbers between 0 and 1, the dimension of a vector space is, I assume, always a natural number. So anything special going on?