One way to handle this is to use temporary tables:
CREATE TABLE tmp_sort (id INT, sort_order INT);
INSERT INTO tmp_sort VALUES (10, 1), (15, 2), (1,3);
UPDATE table, tmp_sort
SET table.sort = tmp_sort.sort_order
WHERE tmp_sort.id = table.picID;
Another way to use control flow:
UPDATE table
SET sort = CASE picID
WHEN 10 THEN 1
WHEN 15 THEN 2
WHEN 1 THEN 3
ELSE sort END
Pay attention to ELSEthe end. If you do not have it, it will set everything else clean!