Is this just a question or do you have data? So experiment 1 predicts A correctly 70% of the time and independently experiment 2 correctly predicts A 70% of the time using a different mechanism. If you had data you could fuse the two groupings of predictors together.

What is the temporality of the tests. I am not a Bayesian, but they would say if one test was performed then the next, you could use the results as the prior (pre-experiment) probability for the next. Do you know the prevalence of the outcome from the population sampled?