The two greatest improbabilities in King Lear are that Lear would not recognize Kent in disguise in Act 1, Scene 4, and that Gloucester would not recognize his own son Edgar who is disguised as a peasant when he becomes his father's guide and protector in Act 4. It is also somewhat improbable that Edgar should be so easily deceived by his half-brother Edmund and suddenly become an outlaw who has to pretend to be a madman. Furthermore, it is improbable that Gloucester should be so easily deceived by Edmund as well.
And there are several glaring improbabilities in Act 1, Scene 1, where Lear asks his three daughters to tell him how much they love him. It is improbable that he could be so easily deceived by Goneril and Regan, who are both declaring their love with such hyperbolic speeches. For example, Goneril says, "Sir, I love you more than words can wield the matter, / Dearer than eye-sight, space and liberty . . ." Regan follows by saying that she loves him even more than that. It is also improbable that Cordelia should be so reticent in expressing her love for her father, since hers is the only genuine love. Tolstoy in discussing this play in an essay titled "Shakespeare and the Drama" says that she seems to be purposely trying to "vex" her father.
It is improbable that Lear and Gloucester should encounter each other in the fields near Dover and that so many of the principal characters should all come together so neatly in that area. It is inconsistent with their characters that Goneril and Regan should both fall in love with Edmund so quickly and that Goneril should kill her sister and then commit suicide. It is inconsistent with his character that Edmund should become so kind and sentimental just before he dies, and that he should try to save Lear and Cordelia after ordering them executed.