You can search in a an array by using the ANY function:
create table numbers as
select * from (
values
(1, array[1,2]),
(2, array[2,3,4]),
(3, array[4,5,6])
)
as numbers(id, positions);
select *
from numbers
where 4 = any(positions);
id | positions
----+-----------
2 | {2,3,4}
3 | {4,5,6}
(2 rows)