In the paper entitled "The effect of varying routing probability in two parallel queues with dynamic routing under a threshold-type scheduling", Kojima et al. derive an expression in the form of a product of powers for the state probabilities of a threshold-type shortest queue problem. In this note it is demonstrated that this expression is essentially more complicated and has the form of an infinite sum of products of powers. In fact, Kojima et al. find the first term in this infinite sum only.