Keywords: improbable, implausible, cannot, can't, may not, unable
As a Verb or Adjective
To not have the possibility, skill or permission to do something. English = (be) unable to.
To be unlikely to be true or happen. English = (be) improbable.
To be not easy to believe or to have little chance of being true, and therefore unlikely to be true or genuine. English = (be) implausible.
Used alone in response to your addressee's comments to mean that you do not believe what they say is true, or possible, or that it really surprises you. English = 'I don't believe it!', 'It can't be (true)!', 'Really!?', and so on.
Used alone in response to an event to mean that you find it difficult to accept or believe. You are surprised. English = 'It isn't possible!', 'It can't be (true)!', and so on.
Used immediately next to a verb (usually before it) to mean that the person or thing you are talking about is not able to do that action or is not allowed to do it. English = cannot, can't, may not.