In that case, the two cancel each other out, and both types of evidence are worthless.
You can run it through Bayes Theorom.
This is like a test that predicts an outcome 70% of the time, but has a 70% false positive rate. The end result is a coin toss that is weighted to be 70% on one side, it doesn't help you find the truth in any way.
0RobinZ
Can you create an example in which you would draw a different conclusion by your procedure than by the procedure outlined in the post?