How to update table1 column from table3, with matching id from table2
Your backticks indicate MySQL, where this syntax works:

UPDATE customer AS c
JOIN   garages  AS g ON g.owner_id = c.id
JOIN   the_cars AS t ON t.car_id   = g.the_car_id
SET    c.car  = t.car
WHERE  c.car IS NULL;


In Postgres you would use a different UPDATE syntax:

UPDATE customer AS c
SET    car  = t.car
FROM   garages  AS g
JOIN   the_cars AS t ON t.car_id = g.the_car_id
WHERE  c.car IS NULL
AND    g.owner_id = c.id;


The FROM clause is not standard SQL.

You have to make sure that the query finds at most one car per customer, or the result is not deterministic.