Recently, face swapping has been developing rapidly and achieved a surprising reality, raising concerns about fake content. As a countermeasure, various detection approaches have been proposed and achieved promising performance. However, most existing detectors struggle to maintain performance on unseen face swapping methods and low-quality images. Apart from the generalization problem, current detection approaches have been shown vulnerable to evasion attacks crafted by detection-aware manipulators. Lack of robustness under adversary scenarios leaves threats for applying face swapping detection in real world. In this paper, we propose a novel face swapping detection approach based on face identification probability distributions, coined as IdP FSD, to improve the generalization and robustness. IdP FSD is specially designed for detecting swapped faces whose identities belong to a finite set, which is meaningful in real-world applications. Compared with previous general detection methods, we make use of the available real faces with concerned identities and require no fake samples for training. IdP FSD exploits face swapping's common nature that the identity of swapped face combines that of two faces involved in swapping. We reflect this nature with the confusion of a face identification model and measure the confusion with the maximum value of the output probability distribution. What's more, to defend our detector under adversary scenarios, an attention-based finetuning scheme is proposed for the face identification models used in IdP FSD. Extensive experiments show that the proposed IdP FSD not only achieves high detection performance on different benchmark datasets and image qualities but also raises the bar for manipulators to evade the detection.