In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was 2/5, and therefore the probability that the Democratic candidate would be elected was 3/5 (the two Independent candidates were given no chance of being elected). It was also estimated that if the Republican candidate were elected, the probabilities that a conservative, moderate, or liberal judge would be appointed to the Supreme Court (one retirement was expected during the presidential term) were 1/3, 1/2, and 1/6, respectively. If a Democratic candidate were elected, the probabilities that a conservative, moderate, or liberal judge would be appointed to the Supreme Court were 4/7, 1/7, and 2/7, respectively. A conservative judge was appointed to the Supreme Court during the presidential term.

Required:

What is the probability that the Democratic candidate was elected?