<p>The probability analysis method, an important alternative to deterministic method in complex geotechnical engineering, offers the advantage of quantifying different sources of uncertainty and their corresponding impacts. However, the interval and fuzziness of geotechnical properties are largely overlooked as existing studies assume geotechnical parameters are random variables over an infinite interval. Here, we introduce information entropy theory to derive an uncertainty calculation formula that considers both variable interval and the coefficient of variation (<i>COV</i>), revealing that the fuzzy uncertainty of the variable gradually increases with the widening of the interval and the increase of <i>COV</i> until convergence is reached. Subsequently, an improved Latin hypercube sampling (LHS) that accounts for the correlation among multidimensional variables is proposed via the Cholesky matrix decomposition method, and the superiority of Category Boosting (CatBoost) algorithm in slope stability prediction is discussed. Based on this, the factors influencing probabilistic slope stability analysis is conducted using the improved LHS combined with CatBoost algorithm-based Monte Carlo simulation (MCS) method. The results indicate that the interval affects the probabilistic slope stability analysis by altering the fuzzy uncertainty of the geotechnical parameters, especially when the interval is less than [<i>μ</i>−3<i>σ</i>, <i>μ</i> + 3<i>σ</i>]. Moreover, <i>COV</i>_<i>φ</i> exerts a more significant influence on the MCS statistical results than <i>COV</i>_<i>c</i>, and under identical interval and <i>COV</i> conditions of the geotechnical parameters, slope stability gradually decreases with increasing correlation coefficient due to the simultaneous reduction in strength parameters. This work offers valuable reference for probabilistic engineering stability analysis significantly affected by material fuzziness and actual intervals.</p>