Funnyman Conan O’Brien and First Lady Michelle Obama put on a show for troops stationed at Al Udeid Air Base yesterday. And judging by this short clip of Conan’s stand-up set — apparently taken by someone in the crowd and sent to John Q. Public blogger Tony Carr, who posted it on his YouTube channel — he left the troops howling with laughter. In his gut-bustingly hilarious rant, Conan eviscerates the base’s restrictions on consuming alcohol and suggests a few tweaks to the military’s policy that seemed … let’s call it warmly received by the crowd. Portions of Conan’s trip will be…