An accurate approximation is developed for the distribution of the instantaneous per-terminal signal-to-noise-ratio (SNR) of a downlink multiuser multiple-input multiple-output system with zero-forcing (ZF) precoding. Our analysis assumes a Ricean fading environment, where we show that the SNR at a given terminal is well approximated by the gamma distribution and we derive its parameters. The analysis relies on densities of an arbitrary eigenvalue and a pair of arbitrary eigenvalues of the uncorrelated complex non-standard, noncentral Wishart matrices. Unlike previous studies, we consider microwave and millimeter-wave channel parameters with a unique Rice factor for each terminal. We demonstrate that stronger line-of-sight adversely impacts the ZF SNR, while increasing the Rice factor variability results in higher peak ZF SNR. Our approximations are insensitive to changes in the system dimension and operating SNRs.