Final answer:
The question seems to contain a mix-up of identities, as none of the mentioned individuals, Sandra Day O'Connor, Sarah Palin, or Pearl M. Hart, pursued careers after being a detective.
Step-by-step explanation:
The question seems to be mistakenly referring to Sonia Sotomayor but mixes references to different persons. Based on the given information, none of the mentioned figures, Sandra Day O'Connor, Sarah Palin, or Pearl M. Hart, sought a career after being a detective, as none were detectives in the first place. The information provided speaks about Sandra Day O'Connor, who became the first female Supreme Court justice, Sarah Palin who pursued a career as a national political figure and consultant for Fox News after serving as governor, and Pearl M. Hart who was the first woman lawyer to practice criminal law in Chicago and was known for her social justice work. It appears there is a mix-up in the question. To correctly answer a question regarding what Sonia Sotomayor pursued after her career as a detective, more precise information about her career path would be needed.