Question: I know there is no such thing as a dumb question but this is: Can you serve contextual based ads via adsense or others on a site that is entirely behind https?

Answer: 
**Update:**

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> We’ve updated the AdSense ad code so that it now supports secure ad serving through Secure Sockets Layer (SSL) on Hypertext Transfer Protocol Secure (HTTPS) web pages. This means that publishers with secure sites, i.e., sites that are served over the HTTPS protocol, can now use AdSense ad code to serve SSL-compliant ads. Examples of secure websites include many financial services sites, e-commerce sites, and social networking sites.
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[Google is aware of the issue but does not offer a properly configured HTTPS version of their code at this time](https://www.google.com/support/adsense/bin/answer.py?answer=10528). It'll work by swapping out http for https, but as mentioned above you'll get various errors in browsers.
Yes, as long as the website is not protected by SSL certificates (in that the client accessing the website needs to have a certificate) Google is perfectly capable of indexing your site for keywords to cater the right ads for your website.

I am not sure if Google makes the adsense code available over SSL as well, if not your visitors will be warned by the browser that the page may contain insecure elements. I do know that their analytics code (For Google analytics) does contain an SSL possibility.

In case you have any more questions, Google's adsense support team/faq will be able to better provide answers to your questions, since you can let them know what site you are talking about!