This article presents a Rayleigh fading channel model of integrated sensing and communication (ISAC), proposes a method of probability fusion integrated sensing and communication (PF-ISAC), derives the PF-ISAC channel model, and theoretically proves that when the sensing signal-to-noise ratio (SNR) approaches infinity, the ISAC model will degenerate into an ideal CSI scenario; When the sensing SNR approaches zero, the ISAC model will degenerate into a scenario where CSI is unknown. The relationship between mutual information and SNR of the PF-ISAC system is given. As the SNR increases, the channel capacity of the mutual information gradually approaches the capacity of the ideal CSI when the channel state information (CSI) is unknown. This article proposes a probability fused maximum a posterior (PF-MAP) detection method and a probability fused maximum likelihood (PF-ML) detection method, and compares them with the MMSE estimation MMSE detection method（MMSE-MMSE）. The results show that PF-MAP performs similarly to MMSE-MMSE at low to medium SNRs, while PF-MAP outperforms MMSE-MMSE at high SNRs. We evaluate the error performance of the PF-ISAC system using entropy error (EE), and the results show that MMSE-MMSE, PF-MAP, PF-ML have significant gaps from the theoretical optimal performance EE; Finally, a scheme for power allocation in ISAC system is proposed. When the total power is given, the performance of two-stage equal power allocation in ISAC system is close to optimal.