Conditional Probability, Independence & Bayes · Superchallenge problem

An urn contains $10$ balls, each red or blue. The number of red balls is unknown: before any draws, each of the values $0,1,2,\dots,10$ is equally likely. Balls are drawn one at a time without replacement. The first two balls drawn are both red. What is the probability that the third ball is also red? Express your answer as a common fraction.