Three horses are competing in a race. The fastest horse wins with a probability of 3/5, the slowest horse wins with a probability of 1/10, and the remaining horse wins with a probability of 3/10. I picked a horse uniformly at random to cheer on before the race started but it ended up not winning. What is the probability I picked the fastest horse?

For integer answers, please input your answer in the first blank and put the integer 1 in the second blank.

For fraction answers, please input your numerator in the first blank and your denominator in the second blank. Answers should be expressed in simplest form as improper fractions if applicable.