InDesign does not include any mobi export filter, only EPUB.
Several versions ago, Amazon developed a mobi export plugin, which was never updated nor adapted for new versions.
If you use PDF in InDesign, they are handled like placed images, not like normal content in InDesign. But with scanned images it makes no difference neither, these are images.
Warning: I don't do any sort of ePub work...
I suspect you might want to run OCR in Acrobat to convert the scanned text to real text, then you at least have more options for what you can do with the pages.
You need to create a new version of your book for a reflowable text ePub, which is quite a different animal from the print version. Briefly: extract the text from the PDF. Create a new InDesign document with an intent of Digital Publishing. Place your text, then style it using Paragraph and Character Styles, and anchor images. Your original pages size is irrelevant as the text is one continuous document and there are no page numbers.
Subsequently you can convert your ePub into a Mobi file, which is the format used for the Kindle. It's best to use the latest version of InDesign (currently CC2014.1) to create ePubs. It's not intuitive and you can learn more about creating ePubs by viewing the excellent Lynda.com tutorial: http://www.lynda.com/EPUB-tutorials/InDesign-CC-EPUB-Fundamentals/143324-2.html
There's also an Adobe InDesign forum for ePubs for specific questions.
For your situation, you could try using alternatives like PDF4Kindle, Calibre, or Papercrop. But based on what I've read and my quick experiment, depending on the complexity of your PDF, it may be more effort than it's worth to try to convert a PDF into a legible Kindle, ePub, or any other e-reader file.
I did a quick test on Calibre with a 16-page PDF that contained multiple columns and images. The results were illegible! It ran the lines from each column together, making the text difficult to comprehend. Calibre explains why PDFs are difficult to convert -- Ebook Conversion — calibre User Manual. I have not tried the other two applications that I suggested above, but I would assume that the results would be very similar.
I don't know what kind of results you got when you converted it in InDesign, but if your first test turned out fine and it was just the size of the file that you are concerned about, you could use Acrobat to reduce your PDF's file size and convert it to the Kindle format in InDesign again.
Hope this helps. Good luck!