Knots can spontaneously form in polymers. How knotting affects polymer behavior depends on polymer knotting probability, p(knot). An intriguing result about p(knot) in recent studies is that p(knot) exhibits a non-monotonic dependence on the bending stiffness and is maximized at L-p approximate to 8a, where L-p is the persistence length and a is the hardcore diameter of the monomer. In this work, we propose a new explanation for the non-monotonic behavior of p(knot) based on the fact that polymer knots are typically localized. We find that the non-monotonic behavior results from the competition of a special entropic effect arising from the variation in the sizes of localized knots and an effect arising from the variation in the free-energy cost of forming a localized knot on a fragment of a polymer. The first effect refers to the situation that shrinking the knot size for a polymer with a fixed length essentially increases the number of "slots" for knot formation and enhances p(knot). Based on this explanation, we derive an approximate analytic equation that captures the non-monotonic behavior of p(knot). Overall, this work provides new insights into p(knot) beyond previous studies, in particular, unifying the effect of the knot size on p(knot) and the effect of the polymer length on p(knot). The results can be applied to understand DNA knotting, considering that the effective L-p/a for DNA can be widely varied by the ionic strength.