with day
AS (SELECT
  user_id,
  DATE_TRUNC('day', datetime) AS active_day
FROM events
GROUP BY 1, 2),
with_first_day
AS (SELECT
  user_id,
  active_day,
  FIRST_VALUE(active_day) OVER (PARTITION BY user_id ORDER BY active_day) AS first_day
FROM day),
with_day_number
AS (SELECT
  user_id,
  active_day,
  first_day,
  (active_day - first_day) / (24 * 60 * 60) AS day_number
FROM with_first_day)
SELECT
  TIME_FORMAT(first_day, 'yyyy-MM-dd') AS first_day,
  SUM(CASE WHEN day_number = 0 THEN 1 ELSE 0 END) AS day_0,
  SUM(CASE WHEN day_number = 1 THEN 1 ELSE 0 END)/day_0 AS day_1,
  SUM(CASE WHEN day_number = 2 THEN 1 ELSE 0 END)/day_0 AS day_2,
  SUM(CASE WHEN day_number = 3 THEN 1 ELSE 0 END)/day_0 AS day_3,
  SUM(CASE WHEN day_number = 4 THEN 1 ELSE 0 END)/day_0 AS day_4,
  SUM(CASE WHEN day_number = 5 THEN 1 ELSE 0 END)/day_0 AS day_5,
  SUM(CASE WHEN day_number = 6 THEN 1 ELSE 0 END)/day_0 AS day_6,
  SUM(CASE WHEN day_number = 7 THEN 1 ELSE 0 END)/day_0 AS day_7
FROM with_day_number
GROUP BY 1
ORDER BY 1