Interarrival times conditional distribution

Suppose that you are the marketing executive of firm selling specialized engineering lubricants. To reconsider your company's marketing strategy you are keen to understand the sales figures in details and hence count the number of times of the occurrence of your sales figure crossing a certain value, say Rs. . Furthermore you know that the distribution of the sales figures crossing this value is Poisson distributed and that exactly one such event has occurred within time , say till the month of June for the financial year starting April. Now we know that a Poisson process has the property of being stationary with independent increments, hence in each interval of a 3 month period, i.e., , which is of equal length, the probability of the sales figure crossing Rs.  is equal. Hence it would mean that for  we would have