The Intern Did It

Late one evening, someone at a prop trading firm propped open the door to the secure server room, a serious compliance breach. A witness comes forward and claims that the culprit was one of the interns.

The witness is right 75% of the time: whichever group the culprit actually belongs to (intern or full-time employee), the witness names that group with probability $3/4$ and the other group with probability $1/4$. One third of the people in the office are interns and two thirds are full-time employees. Before the witness spoke, every person in the office was equally likely to be the culprit.

Given the witness statement, what is the probability that the culprit is an intern? Give an exact fraction.