"improbable task" is correct and usable in written English.
You can use it to describe a task that seems unlikely to be possible or successsful. For example: "I have been assigned an improbable task, trying to teach a cat to do tricks!".
But none seems to believe it can stabilise the place; and this remains NATO's improbable task.
Turning San Francisco into a solar beacon might seem an improbable task, but residents have demanded it.
There appeared little likelihood of Edinburgh overturning the 19-point deficit but they set about that improbable task with vigour.
Basically it's a caper movie: some improbable task has to be pulled off by a combination of ingenuity, training, deception and luck.
9 07 p.m. | Updated The Philadelphia Flyers awoke Monday with the improbable task of figuring out how to rebound from a 3-1 series deficit against the Devils in the Eastern Conference semifinals.
Two days later, Novell and Netscape Communications, a leading Internet-software formedformed a joint venture called Novonyx, whose slightly improbable task is to get big companies to use both firms' (rival) technologies.
Elsewhere he attends to similarly vast and improbable tasks with equally low-tech equipment.
I've seen him accomplish far more improbable tasks and it's worth the effort even if it fails to materialize this cycle.
Now that you have a basis to start from, it's time to get rid of the more impossible or improbable tasks.
As improbable a task as it may seem to make a faceless, squid-like creature lovable, VanderMeer does it.
Given the party's current unpopularity in Scotland, and the clear alternative articulated by the SNP, this seems like an improbable and gargantuan task with just three months to polling day.
