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Requirements completeness is among the most critical and difficult software engineering challenges. Missing requirements often result from poor risk analysis at requirements engineering time. Obstacle analysis is a goal-oriented form of risk analysis aimed at anticipating exceptional conditions in which the software should behave adequately. In the identify-assess-control cycles of such analysis, the assessment step is not well supported by current techniques. This step is concerned with evaluating how likely the obstacles to goals are and how likely and severe their consequences are. Those key factors drive the selection of most appropriate countermeasures to be integrated in the system goal model for increased completeness. Moreover, obstacles to probabilistic goals are currently not supported; such goals prescribe that some corresponding target property should be satisfied in at least X% of the cases. The paper presents a probabilistic framework for goal specification and obstacle assessment. The specification language for goals and obstacles is extended with a probabilistic layer where probabilities have a precise semantics grounded on system-specific phenomena. The probability of a root obstacle to a goal is thereby computed by up-propagation of probabilities of finer-grained obstacles through the obstacle refinement tree. The probability and severity of obstacle consequences is in turn computed by up-propagation from the obstructed leaf goals through the goal refinement graph. The paper shows how the computed information can be used to prioritize obstacles for countermeasure selection towards a more complete and robust goal model. The framework is evaluated on a non-trivial carpooling support system.