Using Bayes' theorem is not an instance of
deductivereasoning. And if you aren't using deductive reasoning, you can't "prove" things. Statistical and probabalistic arguments can be used to demonstrate evidence, not proof.
This argument is known as the probabalistic modus tollens, and it is a logical fallacy (see
Cohen, 1994, p. 998). c does not follow from a and b. E.g., what if the likelihood that a blue state elects Candidate X is 5%? What if there are many more red states than blue states (i.e., what if the prior probability of a state being red is very high)?
The value of Bayes theorem is that it allows us to avoid this line of faulty reasoning, and instead actually calculate values like c (the posterior probability).
Your argument summarised seems to be:
1. Your personal existence would be very improbable if reincarnation does not exist
2. You do personally exist
3. Therefore reincarnation does probably exist
The essential problem I see with your argument is that you are not specifying either (4) the prior probability of reincarnation,
before taking into account your personal existence, nor (5) the conditional probability of your personal existence if reincarnation
does exist. 4 in particular would surely be vanishingly small, considering that there is no plausible physical mechanism via which reincarnation might occur. You need (4) and (5) to apply Bayes theorem here - your argument as it stands is not a Bayesian argument.