Probability of event A given B and C

Question

The best example of this problem I could come up with is a hypothetical MMA match.

Assume the probability that fighter 1 wins by submission (Event B) is $50$% or $0.5$ and the probability that fighter 2 loses by submission (Event C) is $70$% or $0.7$. What would be the probability that fighter 1 beats fighter 2 by submission (Event A)?

Would that be $P(A|(B∩C))$? Also is that the same as $P(A|B) ∩ P(A|C)$? In this case the $P(B∩C) = P(B) * P(C) = 0.7 * 0.5 = 0.35$ which does not make sense. What am I missing?

Or is it as simple as $P(C) + P(B) - P(A∩B) = 0.7 + 0.5 - 0.35 = 0.85$? As in fighter 1 wins by submission or fighter 2 loses by submission?

Answer 1

There is not nearly enough information.

Here are two scenarios showing the figure could range from $0\%$ to $100\%$, and many other scenarios and any intermediate figure is also possible

                                  Scenario 1    Scenario 2 
 
Prob 1 beats 2 by submission            0%          100%
Prob 1 beats 3 by submission           70%           40%
Prob 1 beats 4 by submission           70%           40%
Prob 1 beats 5 by submission           60%           20%
 
Prob 2 loses to 1 by submission         0%          100%
Prob 2 loses to 3 by submission        90%           50% 
Prob 2 loses to 4 by submission        90%           50%
Prob 2 loses to 5 by submission       100%           80%