Christians, how do you explain 'miraculous' things happening to non-Christians?

You are right about miracles. To God, there are no miracles. A miracle describes how we feel when we've witness something truly wonderful and majestic -- God's law in action. Even Jesus said that the works that he did weren't miracles, even though they certainly looked miraculous to everyone else. Jesus said that the works that he did, everyone else could do too. Certainly something to aspire too. And Jesus never said that God's law was only for Christians. God's law applies to everyone.