It's an exercise from the online book Bayes Rules! An Introduction to Bayesian Modeling with R. Thus the book has no chapter with the right answers and so far I've not found a designated place to discuss its exercises, let's do the discussion here:)
Exercise 2.4 (Vampires?) Edward is trying to prove to Bella that vampires exist. Bella thinks there is a 0.05 probability that vampires exist. She also believes that the probability that someone can sparkle like a diamond if vampires exist is 0.7, and the probability that someone can sparkle like a diamond if vampires don’t exist is 0.03. Edward then goes into a meadow and shows Bella that he can sparkle like a diamond. Given that Edward sparkled like a diamond, what is the probability that vampires exist?
Letting B denote the event that vampires exist and $B^c$ denote the event that vampires doesn't exist, we have $$P(B)=0.05$$ and $$P(B^c)=1-P(B)=0.95$$
Letting A denote the event that someone can sparkle like a diamond, we also have $$L(B|A)=P(A|B)=0.7$$ and $$L(B^c|A)=P(A|B^c)=0.03$$
According to the Bayes' rule we can calculate the probability that vampires exist given that Edward sparkled like a diamond $$P(B|A)=\frac{P(B)*L(B|A)}{P(A)}$$ P(A) can be calculated by $$P(A)=P(A|B)*P(B)+P(A|B^c)*P(B^c)=0.7*0.05+0.03*0.95=0.0635$$
Thus the answer is $$P(B|A)=\frac{0.05*0.7}{0.0635}=\frac{70}{127}\approx0.55$$
