We have an M/M/c queue that models customers arriving at a store. The arrivals of customers are Poisson distributed with rate $\lambda=9$. There are three employees serving the customers. The time it takes to serve a customer is exponentially distributed with rate $\mu=0.75$ (i.e. mean $\frac{1}{0.75}=\frac{4}{3}$). We say that an employer is idle if he is not currently serving a customer.
At a given point in time, the store is empty. What is the probability that during the next hour there will always be at least one idle employee? Alternatively, if we let $X(t)$ denote the number of customers in the system at time $t$, we are looking for the probability that $X(t)<3$ for all $0 \leq t \leq 1$ given that $X(0)=0$.
I am not sure how I should approach this problem. I am aware of the transition rate matrix and figured I could combine states 3 and above into one absorbing state, leaving me with the state space $\{0, 1, 2, 3\}$. However I'm unsure how to utilize that.