Google indexing non existing pages

Looks like googlebot visited non-existent page www.domain.com/page.php/sundirectory1/subdirectory2/ and it loaded and indexed same content as for page www.domain.com/page.php what resulted in duplicate content penalty. Basically any non-existent page like www.domain.com/page.php/any-subdirectory-1/any-subdirectory-2/..../any-subdirectory-n/ where n is from 1 to infinity still won't return error but content of page www.domain.com/page.php That results in huge amount of duplicate pages.

My question is what is the reason that such a non existing URLs are returned as actual pages. Is it hosting bug? I checked it on site hosted with different provider and such a non existent URLs return error. And what are the possible solutions? Please do not tell me to include for each of the pages page.php/* into robots.txt or redirect from page.php/* to page.php as the website has 100+ pages and I would have to do it for each new page. And what would be better options SEO wise (I would need google to deindex the duplicate pages ASAP but I guess it will take months anyway), somehow get them to return 404 or do 301 redirect to correct page?

If the solution is more complex and will take your valuable time, shoot me a PM and we can figure out some kind of a paid deal for fixing this problem.

This is the answer I got from my host: " From what you are describing, I understand you are having issues with your site sending duplicate pages to Google search engine. This is something you will have to follow up on with Google. It's because of how PHP builds pages. As something is hit on one page, it creates additional pages. It's fairly common and Google will most likely have some sort of answer for this. Thank you for your understanding with this matter."

Unless you have sexy body and career in sports do not go for hosting at godaddy. It's useless for anything else than selfpromotion.