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A fundamental understanding of the photoexcited carrier system in diamond is crucial to facilitate its application in photonic and electronic devices. Here, we studied the detailed balance between free carriers and excitons in pristine diamond by using a deep-ultraviolet (DUV) pump in combination with terahertz (THz) probe spectroscopy. We investigated the transformation of photoexcited carriers to excitons via an internal transition of excitons, which was newly found to occur at a frequency of approximately 15 THz. We determined the equilibrium constant in the Saha equation from the temperature dependence of the free-carrier density measured at chemical equilibrium. The derived exciton binding energy was larger than the conventional value, which indicated an energy shift due to the fine-structure splitting of the exciton states.