Wrong NULL match results in "Subquery returns more than 1 row" (error code 1242)

DROP TABLE IF EXISTS a;

DROP TABLE IF EXISTS b;

CREATE TABLE a (

	a_id INT(20) UNSIGNED NOT NULL AUTO_INCREMENT,

	b_id INT(20) UNSIGNED NULL DEFAULT NULL,

	c_id VARCHAR(255) NULL DEFAULT NULL,

	PRIMARY KEY (a_id)

)

COLLATE = 'utf8_general_ci'

ENGINE = InnoDB;

CREATE TABLE b (

	b_id INT(20) UNSIGNED NOT NULL AUTO_INCREMENT,

	c_id VARCHAR(255) NULL DEFAULT NULL,

	PRIMARY KEY (b_id),

	INDEX idx_c_id (c_id)

)

COLLATE = 'utf8_general_ci'

ENGINE = InnoDB;

INSERT INTO a (b_id, c_id) VALUES (NULL, NULL);

INSERT INTO b (c_id) VALUES (NULL);

INSERT INTO b (c_id) VALUES (NULL);

UPDATE a SET b_id = (SELECT b.b_id FROM b b WHERE b.c_id = a.c_id);