The EigenAnt Ant Colony System (EAAS) model is an Ant Colony Optimization (ACO) model based on the EigenAnt algorithm. In previous work, EAAS was found to perform competitively with the Enhanced Ant Colony System (EACS) algorithm, a state-of-the-art method for the Sequential Ordering Problem (SOP). In this paper, we extend EAAS by increasing the amount of stochasticity in its solution construction procedure. In experimental results on the SOPLIB instance library, we find that our proposed method, called Probabilistic EAAS (PEAAS), performs better than both EAAS and EACS. The non-parametric Friedman test is applied to determine statistical significance.