Risk Arb Question

I'd look at this as a scenario analysis exercise. For each probable event - merger closing, dividend, bankruptcy, etc. - you should have a basic model with pro-forma capital structure and effect on cash flow / earnings and share price, as well as the resulting upside / downside (and IRR) math for each case. There is really not a scientific way to calculate the probability of any single event taking place, it is generally arbitrarily assigned based on your understanding of the situation (someone who works more closely with risk arb can feel free to correct me). So a merger closing may have a 50% probability, followed by a dividend (assuming special or something) of 30%, and then a 20% chance of bankruptcy which adds up to 100%. From there you can weight the IRR of each scenario based on its probability and arrive at a "probability weighted" IRR or risk/reward ratio. I've used this approach with success both on the job and in HF interviews. 

There are probably some books on risk/merger arb out there that gets into more detail on arriving at the probabilities, but for an interview I think you are likely set by just arriving at your own assumption based on the case. I.e., an announced merger trading at a tight spread with achievable conditions precedent would probably be deserving of a higher probability % of closing.