The Channel Dash in daylight or catching and sinking Bismark without her scoring a single hit on one British ship.or plane. Gaines
Although he wasn't the only one, Tsutomu Yamaguchi surviving the A-Bombing of both Hiroshima and Nagasaki.
Incredible story of the Lancaster pilot who bailed out over Germany whose life was saved when a searchlight helped him find his parachute...which wasn't strapped on http://www.dailymail.co.uk/news/article-2607895/Incredible-story-Lancaster-pilot-bailed-Germany-life-saved-searchlight-helped-parachute-wasnt-strapped-on.html
Here you go. https://books.google.fr/books?id=_VY7AwAAQBAJ&pg=PT191&lpg=PT191&dq=Barry+Douetil&source=bl&ots=XO-gnBN5G1&sig=iSQ1kMNg-937kryA-R74WnQ1LxM&hl=fr&sa=X&ved=0ahUKEwiD8pLduunNAhXI1xoKHRKmCGAQ6AEIazAO#v=onepage&q=Barry%20Douetil&f=false https://www.warhistoryonline.com/war-articles/surviving-wwii-pilot-nearly-died-freefall.html http://www.express.co.uk/news/uk/471272/Wartime-bomber-tells-story-of-narrow-escape-on-Antiques-Roadshow
Most improbable event in WWII: The Japanese raid on Pearl Harbor. The man who planned it had every reason to believe it wouldn't work. The raid used six carriers, about four more than had been used in any attack to date. The Japanese weren't thought capable of at-sea refueling of large forces over long distances. The commanders on the ground violated a laundry list of rules in the months before Dec. 7th. The Japanese spies working out of their embassy had free run of the island, including the areas around Pearl Harbor. The Public Works officer on Oahu refused to release the newly constructed Air Information Center to the Airedales in time for them to work up the procedures. There was a former Eagle Squadron commander on loan from the USN who could have trained them up nicely if given the time.
Not sure I would call that the most improbable event of the War. First the US wargamed it 'live' I believe before the war., and Japan had a history of executing sneak attacks on ships in port as a opening act in a war.
The '39 Fleet exercises was an attack on Pearl, but it was gamed as an attack on an enemy harbor, not on Hawaii specifically. And, yes, Japan had a habit of attacking before a declaration, which is why I left that off the list.
No question that for US command/leadership the strike on Pearl Harbor was a surprise, but is that enough to make it the most improbable event of WWII? Germany moving large mobile forces through the Ardennes in 1940 and later in 1944 was a surprise to Allied command/leadership, granted for different reasons. Is surprise alone enough? The failures of American leadership can be summed up to 4 very commonplace human failings Arrogance, Complacency, Bureaucracy and a unwillingness to yield the American ideals even in the face of real danger. All could be said of 9/11. Tom Clancy wrote Debt of Honor in 1994 which culminated with a airliner being crashed into the Capitol building, The FBI had reports of Arab foreign nations learning to fly large aircraft, yet showing little interest in learning how to land them and the US loses track of several of the hijackers after their visa expired, despite a stated goal of Al Qaeda to do something spectacular on US soil. I would nominate Doolittle's raid as more improbable. Successfully launching 16 twin engine medium bombers from a WWII era carrier under combat conditions in the face of a aroused enemy and actually hitting most of their targets and without losing any aircraft to enemy action.