Although supervised machine learning classification techniques have been successfully applied to detect collapsed buildings, there is still a major problem that few publications have addressed. The success of supervised machine learning strongly depends on the availability of training samples. Unfortunately, in the aftermath of a large-scale disaster, training samples become available only after several weeks or even months. However, following a disaster, information on the damage situation is one of the most important necessities for rapid search-and-rescue efforts and relief distribution. In this paper, a modification of the supervised machine learning classification technique called logistic regression is presented. Here, the training samples are replaced with probabilistic information, which is calculated from the spatial distribution of the hazard under consideration and one or more fragility functions. Such damage probabilities can be collected almost in real time for specific disasters such as earthquakes and/or tsunamis. We present the application of the proposed method to the 2011 Great East Japan Earthquake and Tsunami for collapsed building detection. The results show good agreement with a field survey performed by the Ministry of Land, Infrastructure, Transport and Tourism, with an overall accuracy of over 80%. Thus, the proposed method can significantly contribute to a rapid estimation of the number and locations of collapsed buildings.