Try this:
DECLARE @customer TABLE(Customer VARCHAR(50), account int, [rank] int)
INSERT INTO @customer (Customer, account, [rank])
VALUES('a',1,0),
('b',2,1),
('a',3,3),
('a',4,2),
('c',5,0)
UPDATE t1 SET [rank] = t2.MaxRank
FROM @Customer t1 INNER JOIN
(
SELECT Customer, MAX([rank]) MaxRank
FROM @customer
GROUP BY Customer
) t2
ON t1.Customer = t2.Customer