According to Google you will need to modify how that page works for Adsense to properly handle them:
Our AdSense crawlers index each individual URL containing the AdSense
ad code in order to deliver relevant ads to that page. If your site is
dynamically generated using a program language such as PHP or is
created using information from a database, we'll still be able to
target each unique URL with ads specific to the content of that page.
However, the following types of dynamic sites may need modification to
receive targeted ads:
Dynamic pages that use the POST method for form submission Sites using
the POST method use the same URL for many different content pages. To
allow us to target the content of each unique page, we recommend that
you change these pages so that your variables are passed through the
URL using the GET method.
I'm guessing they will use the keywords in the query string to help them determine what ads to show and/or once the page is loaded for the first time they will know to crawl it with those parameters in the query string which will show them the content of that page which will allow them to server relevant ads going forward.