One important issue in cognitive transmission is for multiple secondary users to dynamically acquire spare spectrum from the single primary user. The existing spectrum sharing scheme adopts a deterministic Cournot game to formulate this problem, of which the solution is the Nash equilibrium. This formulation is based on two implicit assumptions. First, each secondary user is willing to fully exchange transmission parameters with all others and hence knows their complete information. Second, the unused spectrum of the primary user for spectrum sharing is always larger than the total frequency demand of all secondary users at the Nash equilibrium. However, both assumptions may not be true in general. To remedy this, the present paper considers a more realistic assumption of incomplete information, i.e., each secondary user may choose to conceal their private information for achieving higher transmission benefit. Following this assumption and given that the unused bandwidth of the primary user is large enough, we adopt a probabilistic Cournot game to formulate an opportunistic spectrum sharing scheme for maximizing the total benefit of all secondary users. Bayesian equilibrium is considered as the solution of this game. Moreover, we prove that a secondary user can improve their expected benefit by actively hiding its transmission parameters and increasing their variance. On the other hand, when the unused spectrum of the primary user is smaller than the maximal total frequency demand of all secondary users at the Bayesian equilibrium, we formulate a constrained optimization problem for the primary user to maximize its profit in spectrum sharing and revise the proposed spectrum sharing scheme to solve this problem heuristically. This provides a unified approach to overcome the aforementioned two limitations of the existing spectrum sharing scheme.