Sale price above 15000 given a 9000 reserve

A seller accepts the first offer of $9000 or more for his car. Offers are i.i.d. exponential with mean $5000. Conditional on the car being sold, the probability that the sale price is at least $15000 can be written as $e^{a}$ with $a$ rational. Find $a$.

$a=-6/5$. The accepted bid is distributed as a bid conditioned on exceeding $9000. By memorylessness, $\mathbb{P}(B\ge15000\mid B\ge9000)=\mathbb{P}(B\ge6000)=e^{-6000/5000}=e^{-6/5}$.