A lot of tests, scans and the like. If they weren't able to determine the cause of the cardiac arrest, literally the sudden cessation of operations of that muscle, then it's just as likely to have been a one off as something that will happen again.
If some of the tests show that his heart wasn't damaged, is otherwise strong and can take the demands of physical activity then there isn't a lot to worry about. The defib implant will jolt the heart back into action immediately if he has another arrest, which massively reduces the likelihood of him suddenly dying again.
This is a completely different situation from heart attack (which usually results when your arteries are fecked and your heart doesn't get enough blood), and heart failure (when your heart can't pump blood effectively). Both of those conditions are likely to repeat or worsen with or without treatment and putting strain on the heart with physical activity is dangerous for either situation.