Estimating the probability of the residual lifetime based on Kaplan-Meier curve

So I had this question on my exam about survival analysis and I didn't know the answer but I would like to know how I should answer it:

"Give, based on this KM-curve, an estimate for the probability that the residual lifetime is larger than 300 days, when the patient is already standing on the waiting list for 500 days?"

Can I use this equation: P(T > waiting 800 days) = P(T > waiting 500 days) X P(T > waiting 300 days | T > waiting 500 days) and then use the KM-curve to find the probabilities of waiting more than 800 days and waiting more than 500 days? Or is there a better way to do this?

I also had to give an estimate for the standard error of this probability by using the delta-method. But how can I do this?