This paper considers computational costs that occur when a cognitive radio system changes channels for a secondary user. The theoretical gain was estimated to find ways to optimize computations, based on knowledge about the conditional state of the cognitive radio system. The analysis of the unnormalized matrix of transition probabilities made it possible to formulate two rules for filling the matrices. The authors studied the structure of the matrix of transition probabilities for three channels and tried to identify the relationship between its elements and symmetry for the matrix dimensions - 24 to 24 elements. The proposed technique allows replacing the calculation of the product of N real numbers with one rewriting of the real number and reduces the multiplication operations. The results of the work can serve as methods for optimizing computational costs in cognitive radio systems or similar systems, this is due to the need to perform computations on devices that do not have enough free resources.