You could use three queries, but then you would need to add some sort of a "submit" or trigger for each level.
So with the first method, the first thing to do is to populate the "province" field... but you will only want each province listed once... so you would query for all records but for the province, make sure you use the "UNIQUE" SQL command sort of like this:
SELECT UNIQUE(province) AS provinceList FROM yourTable
Then you would repeat region or loop through your results of the provinceList column to give you your dropdown names and values.
Then once submit is pressed, the next round will involve query the results based on the province... something like this:
SELECT * WHERE province = "$_POST['dropdownName']"