A method and an apparatus for determining primary and secondary escape probabilities for a large photon-counting detector without pile-up. A model for the detector with no pile-up is formulated and used for spectrum correction in a computed tomography scanner. The method includes computing primary K-escape and secondary K-escape probabilities occurring at a certain depth within the photon-counting detector. Further, a no pile-up model for the photon-counting detector is formulated by determining a response function, based on the computed primary and secondary K-escape probabilities and geometry of the photon-counting detector. The method includes obtaining a measured CT scan of an object and further performs spectrum correction by determining the incident input spectrum based on the response function and the measured spectrum of the large photon-counting detector.