$ids = array(1, 2, 3, 4);
$ids = join(', ', $ids);
$query = "SELECT * FROM business WHERE business_id IN ($ids)";
// $query => SELECT * FROM business WHERE business_id IN (1, 2, 3, 4)
The usual SQL injection warnings still apply, you may want to loop through the ids first to validate or escape them. Also, if you expect strings instead of numbers, use this:
$ids = array('a', 'b', 'c', 'd');
$ids = join("', '", $ids);
$query = "SELECT * FROM business WHERE business_id IN ('$ids')";
// $query => SELECT * FROM business WHERE business_id IN ('a', 'b', 'c', 'd')