Conditional Probability, Independence & Bayes · Challenge problem

In a town, a sunny day is followed by a sunny day with probability $\tfrac34$ and by a rainy day with probability $\tfrac14$; a rainy day is followed by a rainy day with probability $\tfrac12$ and by a sunny day with probability $\tfrac12$. Today (day $0$) is sunny. Given that it rains on day $3$, what is the probability that it rained on day $1$? Express your answer as a common fraction.