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In this paper, we propose a probabilistic preemption scheme in cognitive radio networks that will simultaneously ensure the primary user (PU) packets' Quality of Service (QoS) and the secondary user (SU) packets' transmission continuity. This scheme differs from a complete preemption scheme or a complete non-preemption scheme in conventional cognitive radio networks in that a PU packet can interrupt an SU packet's transmission and preempt the channel with a certain probability that is termed the preemptive probability. In order to decrease the possible negative influence of SU packets on PU packets' QoS, we introduce an access threshold, i.e. a limit on the size of the SU packet buffer, which controls the access of the SU packets. As part of the mathematical analysis of the probabilistic preemption scheme, we establish a discrete-time priority queueing model and then characterize it by a two-dimensional Markov chain. Based on the steady-state solution of the system we give formulas for several performance measures of the network users. We also provide numerical results to highlight the influence of the preemptive probability and the access threshold on the system performance. Moreover, we also compare the system performance of the proposed probabilistic preemption scheme with the preemptive and non-preemptive schemes by using numerical results. Finally, we build an optimization framework by the help of properly chosen net benefit function to optimize the preemptive probability and the access threshold jointly. [ABSTRACT FROM AUTHOR]