Selecting eggs from the grocery store

Suppose you’re at the grocery store looking to buy some eggs. Each egg carton holds 12 eggs. You’re given the following information regarding the state of the eggs inside:

• There is a 60% chance that all the eggs are unbroken
• There is a 30% chance that exactly one egg is broken
• There is a 10% chance that exactly two eggs are broken

You buy a carton of eggs, and take out your first egg only to discover that it’s broken. Given this, what’s the probability that there is one additional broken egg in the holder?