The 'Lighter' Side Of The Force
The answer is simple. It was in the script.
I know you all we'll think it over after you read this: I was re-watching the scene again but on the film instead, and you can hear Palpatine say "I must say you're here sooner than expected." and we all know that Palpatine had foreseen the future. Since he must have know the future, he must have known that Mace and the three Jedi with him would've either killed him or arrested him and must have been practicing on how to defeat them for a very long time before Revenge of the Sith and order 66, thus he didn't know that Anakin would've showed up later and kill Mace. But because the Jedi Counsel decieded to let Anakin spy on Palpatine because they had become closer, they changed the outcome of the future and because Anakin got to learn that he could save Padmes life, and he found out that Palpatine was the Sith Lord since he told in his chamber and he reporting it to Mace. Thus Anaking siding with Palaptine (Sith/Empire). But we all know that it was a script and you never know the story behind it. But I think that George Lucas has a very great story-telling, without revealing the meaning of every scene.But that's only explanation of how Palpatine could deafet the three jedi that easy and why I believe that Anakin chose to join the dark side. He was manipulated by the Jedi counsel and Palpatine. Had'nt Anakin been apart of the spying and hadn't showed up in Palpatines chambers I believe that when Palaptine would've killed Mace and the three Jedi either way, since he had foreseen them coming. But after the fight he would've gone to Anakin turned him to the dark side, by telling him that the Jedi tried to assassinate him and that they would now be traitors the Republic. I think that George Lucas wants the audience to either have a imagination like I've or there's more to the story. I would've wanted a way longer movies about Star Wars, since it's a huge universe with alot of years passing by. Of course the comics and novels are a great help to cover some gaps between the films.