MySql conditional order by

I have this table (simplified):

CREATE TABLE `my_table` (
  `id` INT NOT NULL AUTO_INCREMENT ,
  `item_name` VARCHAR(45) NULL ,
  `price` DECIMAL(10,0) NULL ,
  PRIMARY KEY (`id`) 
)

I need to select all items from the table, ordered this way:

1. items with price > 0.00 first, ordered by price ASC
2. items with price = 0.00 last, ordered by id

I tried this:

SELECT * 
FROM my_table 
WHERE 1  
ORDER BY 
  CASE price WHEN !0.00 THEN price 
   ELSE id
  END 
ASC

And I get results like

How do I build the query to have

Thank you for your time