Island operation of a microgrid increases operation survivability and reliability when there is a large accident in a main grid. However, because a microgrid typically has limited generation capability, a microgrid operator (MGO) has to take the risk of island operation into account in its market participation and generation scheduling to ensure efficient operation. In this paper, a microgrid islanding event is interpreted as a trade suspension of a contract, and a set of islanding rules is presented in the form of a market rule. The risk of island operation is evaluated by modeling the microgrid islanding stochastically using an islanding probability function, which is defined in the form of a conditional probability to reflect the influence of outside conditions. An optimal bidding strategy is obtained for the MGO by formulating and solving an optimization problem to minimize the expected operating cost. The effectiveness of the proposed method was investigated by numerical simulations in which the proposed method and two other methods were applied to the same microgrid. Numerical sensitivity analyses of the coefficients of the islanding probability function were conducted to determine how an MGO copes with changes in outside conditions.