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.