The progress of modern detector arrays was based on their good angular resolution, which has a great impact on gamma-ray spectroscopy with relativistic fragmentation beams and, thus, allows studies of the most exotic nuclei and discovery of superdeformed states of high spins. Recently, a fast timing array was designed for the future Facility for Antiproton and Ion Research for studying the very short-lived nuclei (of several subnanoseconds) at the extremes of existence. For this purpose, several gamma-ray detector array geometries were designed and simulated to maximize the solid angle and enhance the timing precision and efficiencies. Therefore, the probability correction approach has been applied in the present work to calibrate the newly designed gamma-ray conical array for the fast timing array. The calculated full-energy peak efficiency values for the array were compared to the simulated ones by the GEANT 4 code published in the literature. Results showed a reasonably low-percentage relative difference between the calculated and the reported simulated results <4.5% on average.