I am learning about chemical kinetics and dynamics and as I understand for a general chemical reaction $$\ce{aA + bB -> cC + dD} $$ whose reaction rate, r, can be described by an elementary rate law can be written as follows: $$r= k[\ce{A]^a[\ce{B}]^b} $$
What I do not seem to conceptually understand is if you look at a chemical reaction from a collision theory standpoint, would it not be true that as one reactant that is in a higher stoichiometric ratio relative to the other, the probabilty that the reactants collide (assuming any collision gives a reaction) would be inversely proportional to the stoichiometry of the reactant. For example in the following: $$\ce {A + 2B -> C} $$
You basically need 2 mols of B for every mol of A for a successful reaction to produce C, so if the probability that A successfully collides with a mol of B is $\propto$ to $1/z$, then the probability that A successfully collides with TWO mols of B $\propto 1/z^2$ which is lower, so why does a reaction rate, which is $\propto$ to the probability of a collision, with an elementary rate law $\propto$ to a concentration raised to an exponent?