A radio telescope captures strong signals from a Nova in Poisson process at an average rate of $144$ per day. If it is known that the first such signal will be captured between $5$ hours and $10$ hours, what is the probability that the first such signal will be captured in less than $8$ hours?
My approach: I know that $at=k$, so here it is seemingly conditional probability that probability it will happen before $8$ hour given it happens between $5$ and $10$ hours. But my doubt is here t is constantly changing. So how do I proceed? Should I consider individual cases like it happens at $5^{\text{th}}$ hour, $6^{\text{th}}$ hour, $7^{\text{th}}$ hour etc or is there some other way?