The number 52 is written as a sum of three natural numbers 52 = a + b + c (the triple (a, b, c) is ordered; e.g., the decompositions 52 = 14 + 15 +23 and 52 = 15+23+ 14 are different. Also, assume that all the decompositions have equal probability.) Given that there exists a triangle with sides a, b, and c, what is the probability that this triangle is isosceles?

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