Cognitive radio technology necessitates accurate and timely sensing of primary users' activity on the chosen set of channels. The simplest selection procedure is a simple random choice of channels to be sensed, but the impact of sensing errors with respect to primary user activity or inactivity differs considerably. In order to improve sensing accuracy and increase the likelihood of finding channels which are free from primary user activity, the selection procedure is modified by assigning different sensing probabilities to active and inactive channels. The paper presents a probabilistic analysis of this policy and investigates the range of values in which the modulation of sensing probability is capable of maintaining an accurate view of the status of the working channel set. We also present a modification of the probability modulation algorithm that allows for even greater reduction of sensing error in a limited range of the duty cycle of primary users' activity. Finally, we give some guidelines as to the optimum application ranges for the original and modified algorithm, respectively.