In this paper, we study a spectrum sharing based cognitive radio network (CRN) where secondary users (SUs) share the same spectrum with a primary user (PU) over block fading channels. We assume complete perfect channel state information (CSI) at the SUs while only local instantaneous CSI is assumed at the PU. The PU is assumed to adopt an ON/OFF power allocation based on truncated channel inversion and convey this one-bit side information to all SUs. Based on these assumptions, we investigate the optimal probabilistic power allocation that seeks to maximize the system utilities for SUs subject to the primary interference power constraint, and the secondary rate outage constraints and the peak power constraints. The probabilistic power allocation problem was first reformulated as a non-convex deterministic power allocation problem. To handle the non-convex constraints, we proposed a successive convex approximation (SCA) algorithm that provides high-quality approximate solutions. Convergence analysis on the algorithm was also provided. To further reduce complexity, a decentralized version of the SCA algorithm was proposed. Extensive simulations validated our analyses and demonstrated that superior performance is indeed achieved by our proposed algorithms where the achieved utilities are close to the optimal values.