When the sky reaches the ground

$\large \lfloor x+0.7 \rfloor = \lceil x-0.7 \rceil$

If $$x$$ is a real number chosen between the interval $$[a, b]$$, $$a$$ and $$b$$ being positive integers, find the probability that $$x$$ satisfies the equation above.

 Notations: $$\lfloor \cdot \rfloor$$ denotes the floor function and $$\lceil \cdot \rceil$$ denotes the ceiling function.

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