Provide a comprehensive analysis of the Simulation Hypothesis. Start by outlining Nick Bostrom's trilemma regarding the existence of post-human civilizations and their desire to run ancestral simulations. Discuss the statistical probabilities assigned to each leg of the trilemma. Then, explore the philosophical implications: if we are in a simulation, what does that mean for concepts of free will, objective morality, and the nature of existence? Finally, propose potential methods or empirical tests that could theoretically falsify or validate the hypothesis.