I would say no 'a' because you are using the generic "People" and "by". In the not so distant future, "People will probably go to work by flying car". It can easily be changed though to "Helen will probably go to work in a flying car"

"People will probably go to work by flying car." Just like we say "I get to work by car" or "by train" or "by bike," we'd say "by flying car."

I'd definitely use the (a)