Postgres NOT in array

SELECT COUNT(*) FROM "messages" WHERE NOT (3 = ANY (recipient_ids))

You can always negate WHERE (condition) with WHERE NOT (condition)

You could turn it around a bit and say "3 is not equal to all the IDs":

where 3 != all (recipient_ids)

From the fine manual:

9.21.4. ALL (array)

expression operator ALL (array expression)

The right-hand side is a parenthesized expression, which must yield an array value. The left-hand expression is evaluated and compared to each element of the array using the given operator, which must yield a Boolean result. The result of ALL is "true" if all comparisons yield true (including the case where the array has zero elements). The result is "false" if any false result is found.