We developed a probabilistic theory of transport-reaction processes over various types of configurations of catalytic particles, particularly for a single particle. The theory describes a single pulse-response experiment which is similar to the single pulse temporal analysis of products (TAP) experiment. The analysis is based on the general theory of Brownian motion with "killing" and the Feynman-Kac formula. Different diffusion-reaction problems, particularly the problem "diffusion-very fast reaction" (infinite rate reaction), have been analyzed. In the latter case, the probability for a reactant to be converted equals a purely geometric characteristic, namely, the probability for a reactant molecule to hit at least one catalyst particle in a configuration of particles. Solving a boundary value problem, the probability of conversion can be found as a function of the apparent kinetic parameter. Based on experimental data on exit flow and conversion this parameter can be extracted. Experimental data in studies of CO oxidation over a single particle of Pt catalyst show a qualitative agreement with data from computational experiments based on the developed probabilistic theory. For two-particle catalyst configurations. it was found computationally a non-trivial dependence of the reactant conversion on some geometric characteristics, especially the distance between particles. A distance was found for which conversion is highest. (C) 2008 Elsevier Ltd. All rights reserved.