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In a spectrum sharing scenario, when the channel state information (CSI) of interference links is imperfect, the transmission of the secondary user (SU) may cause a harmful interference on the primary user (PU). To quantify the impact of imperfect CSI on the PU, we present a performance metric termed as interference probability and derive the exact closed-form expression for interference probability of the PU. It is shown that the PU's interference probability is always equal to 0.75 when the CSI of interference links is imperfect. In order to guarantee the PU's interference probability below an acceptable value, a back-off power control mechanism is adopted. Then, under the PU's interference probability constraints, the exact outage probability of partial amplify-and-forward (AF) relay selection scheme in the cognitive relay networks is derived. Finally, numerical results are provided to validate our analysis.