The paper presents an energy efficient WiFi-based indoor positioning algorithm, based on the probabilistic fingerprinting method, suited to be used over smartphone platforms. The work proposes a simple algebraic approach aimed at reducing the computational and energy loads of the probabilistic fingerprinting, which is employed to carry out the position of a smartphone on the basis of the captured WiFi Access Points signal strengths in an indoor area. The presented solution does not apply any kind of approximation with respect to the traditional approach, so avoiding accuracy detriment. The idea is to factoring out the parts of the probabilistic fingerprint formulae that can be computed a-priori, so reducing the computational burden of the positioning process. The paper also highlights the effectiveness of the proposed solution by evaluating the energy saved in comparison with the traditional approach. The obtained results, collected by testing three different smartphones, show that our approach allows saving a significant quantity of energy so increasing the smartphones battery lifetime.