ABSTRACT The automatic classification of X-ray detections is a necessary step in extracting astrophysical information from compiled catalogues of astrophysical sources. Classification is useful for the study of individual objects, statistics for population studies, as well as for anomaly detection, that is, the identification of new unexplored phenomena, including transients and spectrally extreme sources. Despite the importance of this task, classification remains challenging in X-ray astronomy due to the lack of optical counterparts and representative training sets. We develop an alternative methodology that employs an unsupervised machine learning approach to provide probabilistic classes to Chandra Source Catalog sources with a limited number of labelled sources, and without ancillary information from optical and infrared catalogues. We provide a catalogue of probabilistic classes for 8756 sources, comprising a total of 14 507 detections, and demonstrate the success of the method at identifying emission from young stellar objects, as well as distinguishing between small- and large-scale compact accretors with a significant level of confidence. We investigate the consistency between the distribution of features among classified objects and well-established astrophysical hypotheses such as the unified active galactic nucleus model. This provides interpretability to the probabilistic classifier. Code and tables are available publicly through GitHub. We provide a web playground for readers to explore our final classification at https://umlcaxs-playground.streamlit.app.