from fractions import Fraction
from itertools import permutations
balls = [("R", i) for i in range(4)] + [("B", i) for i in range(3)]
pairs = list(permutations(balls, 2))
eligible = [p for p in pairs if any(ball[0] == "B" for ball in p)]
favourable = [p for p in eligible if p[0][0] == "R"]
assert len(pairs) == 42
result = {"conditional_probability": str(Fraction(len(favourable), len(eligible))),
          "eligible_pairs": len(eligible), "favourable_pairs": len(favourable)}
import json
print(json.dumps(result, ensure_ascii=False, sort_keys=True))