Write SQL query to solve given problem: What is the percentage of the number of 4-year public schools from Madison Area Technical College's home state in the Alabama?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT CAST(COUNT(DISTINCT CASE WHEN T1.state = ( SELECT T1.state FROM institution_details AS T1 INNER JOIN state_sector_details AS T2 ON T2.state = T1.state WHERE T1.chronname = 'Madison Area Technical College' ) AND T1.level = '4-year' AND T1.control = 'Public' THEN T1.chronname ELSE NULL END) AS REAL) * 100 / COUNT(DISTINCT CASE WHEN T2.state = 'Alabama' THEN T1.chronname ELSE NULL END) FROM institution_details AS T1 INNER JOIN state_sector_details AS T2 ON T2.state = T1.state