This paper develops a probability distribution from the migration-modified stochastic logistic growth model (MM-SLGM) to analyse the long-term behaviour of population dynamics under demographic uncertainty. By incorporating net migration and stochastic perturbations into the classical logistic model, it derived a stationary probability distribution called the NKIKE distribution that captures the randomness inherent in real-world population growth, particularly in developing economies. The study explored the properties of the developed model, its parameters and simulated its applicability. The resulting distribution, named the NKIKE distribution, provides critical insights into probable population outcomes, thresholds and the effectiveness of policy interventions. This approach bridges theoretical modelling and practical population control strategies, offering a flexible and robust tool for demographic planning amid socioeconomic and environmental fluctuations.