b)What is the probability that 4 customers arrive between 8:30 and 9:00 a.m., if exactly 8
customers arrived between 8:00 and 9:00 a.m.?

In the main body of the question, I'm given that the interarrival process is exponentially distributed with mean of 5 minutes. so I found rate ƛ = 1/5 arrivals per min. But for the question, how do I use conditional probability while accounting for the overlap in time overlap? I have found the individual probabilities of 4 customers arriving between 8:30 and 9 and the probability that 8 arrive between 8:00 and 9:00. How would I go about solving the rest? Would I need to adjust the rate of 1/5 that I was using based on the conditional statement or would I completely disregard the condition based on the memoryless property of the Poisson process?

Thanks