UPDATE customers AS customers_to_update
SET last_event_at = (
  SELECT last_event_at FROM (
    SELECT customers.id, IFNULL(last_events.last,customers.created_at) as last_event_at
    FROM customers
    LEFT OUTER JOIN (
      SELECT customer_id, MAX(events.created_at) AS last
      FROM events
      GROUP BY customer_id
    ) AS last_events
    ON customers.id = customer_id
  ) AS update_map
  WHERE customers_to_update.id = update_map.id
)