A system models human preference between two generated responses, A and B, for a given prompt. It does this by first assigning a numerical reward score to each response, r(A) and r(B). The probability that response A is preferred over B is then calculated as Sigmoid(r(A) - r(B)). Based on this model, what happens to the predicted probability of preferring response A as the difference r(A) - r(B) becomes a very large positive number?

Interpreting Reward Model Scores

A preference model calculates the probability of response 'a' being preferred over response 'b' using their respective reward scores, r(a) and r(b). The initial formula is given as: P(a > b) = exp(r(a)) / (exp(r(a)) + exp(r(b))). Arrange the following algebraic steps in the correct order to simplify this expression into the form Sigmoid(r(a) - r(b)).