I have noticed that when a Poisson distribution has an integer value of $\lambda$, the following holds: $$ \mathbb{P}[X = \lambda] = \mathbb{P}[X = \lambda - 1] $$
I have been able to prove this rather simply using an algebraic method. However, my question is, is there an intuitive reason for why this is the case? For example, if an average of 10 phone calls are received an hour, why is it that 10 phone calls are equally likely as 9 phone calls?