This paper investigates the probability distribution of the signal-to-interference noise ratio (SINR) for a 6G communication system comprising a multi-antenna transmitter, an intelligent reflecting surface (IRS) and a remote receiver station. A common assumption in the literature is that the density distribution function for SINR and signal-to-noise ratio (SNR) of an IRS-to-ground communication follows a Rayleigh and Rician distribution. This assumption is essential as it influences the derivation of the properties of the communication system such as the physical layer security models and the designs of IRS controller units. Therefore, in this paper, we present an analytical derivation for the density distribution functions of the SINR for an IRS-to-6G ground communication ameliorating the typical assumptions in the literature. We demonstrated that the SINR density function of an IRS-to-6G ground communication contains a hypergeometric function which defines the solution to a second-order linear ordinary differential equation (ODE) with 3 points. We further applied the derived density distribution function to determine the average secrecy rate for passive eavesdropping.