CONVERT: Adobe Digital Edition to normal PDF?

OK how do I convert it to be able to read it on my Kindle which supports DRM ebooks - but as it seems not the one from Adobe ?!

"ebook" is not a format & it is the format that is key.
Kindle does not (currently) "do" EPUB.
See: http://www.amazon.com/gp/help/customer/display.html?nodeId=200505520&#recognize
DRM ebooks, for Kindle, use the Kindle DRM scheme for AZW files.
To view an "ebook", whose publisher applies DRM, on Kindle I suspect that you will have to obtain it from the Kindle book library .

An Adobe DRM'd document can only be viewed via Adobe Digital Editions (ADE)
ADE is part of a "package" to assure the intellectual property rights of a publisher are protected.
Summarizing information provided by Jim Lester over in the Adobe Digital Editions Forum:
( http://forums.adobe.com/community/adobe_digital_editions )

--| The .acsm file isn't the book - it a purchase ticket that allows you to download the book.
--| Content Server 4 protected ebooks can not be opened in either Adobe Acrobat or Adobe Reader and can only be opened in Digital Editions.
(An eBook publisher would use Adobe's Content Server to apply Digital Rights Management (DRM) to the PDF/EPUB)
--| "Can I view a Adobe DRM'd document (.ePub or PDF) in a program other than Adobe Digital Editions?" — The answer is: No.
(No legitimate "convert" to a non-DRM PDF/EPUB either - being able to do so would defeat the purpose of publishing with DRM.)

The following file formats can be converted for the Kindle (AZW):
--|  Unprotected PDF (so, *no* DRM applied)
--|  TXT
--| Unprotected MOBI (so, *no* DRM applied)
--|  PRC natively
--|  HTML, DOC, RTF, JPEG, GIF, PNG,  or BMP

Calibre can convert a non-DRM PDF or EPUB file into the unprotected Mobipocket format that the Kindle can read.

A useful reference for users of eReaders is at:
http://en.wikipedia.org/wiki/Comparison_of_e-book_formats
Scroll down to the "Supporting Hardware" table to view what formats a device supports.

Be well...