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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