How to debug variables inside function invoked via ajax call?
The sites/default/files/civicrm/ConfigAndLog/ directory should contain your CiviCRM debug log (and some other files), provided that you're using Drupal, that your Drupal multisite directory is "default", and that the webserver is able to write to that directory. If you're not seeing that, you could:


Check assumptions of what CRM_Core_Error::debug_var() will do with the input you're handing it (eg, check that if you pass in a string like SNORK instead of an array, you see that same word appear in a logfile). ::debug_var() looks like it does print_r
tail -f /path/to/*.log might reveal which logfiles are being printed to when you hit that endpoint.
Check the multisite directory is what you think (should be the same as your settings.php and civicrm.settings.php)
Check again for typos (I see defaut in your question, but that's probably not it!)
Check that the sites/default/files/ directory and its descendant directories are writable to the webserver (typically user www-data, httpd, _www etc)
Double check usage of the debug functions - there have been docs inconsistencies which might lead you astray.
Check out CiviCRM docs on debugging
There are other SE questions on debugging, eg tips on debugging when you can't view page output also applies well to AJAX callbacks etc where you can't/shouldn't modify page output.


CiviCRM has a more modern log interface available in Civi::log()-&gt;debug('debug info'); (see How to print variable/debug data from your extension.php? for an answer on that).

If even that doesn't work, you could fall back to "stock" PHP debugging methods like error_log() and file_put_contents() if CiviCRM debugging isn't working.