Colourful Squares

Probability Level 5

The squares of a 3×33 \times 3 grid of unit squares are coloured randomly and independently so that each square gets one of 5 colours. Three points are then chosen uniformly at random from inside the grid. The probability that these points all have the same colours can be expressed as ab\frac{a}{b}, where aa and bb are coprime positive integers. What is the value of a+ba+b?

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