Possible Clues:

• Figured (out), in slang
• Puzzled (out)
• Having lost half original value, scooter's given something to improve running
• Administered a narcotic
• Figured (out), slangily
• Like some rule-breaking Olympians
• Subject to removal from the horse race
• 'Nature had it all -- out for me to be the Belle of Hicks Corners' (P. G. Wodehouse, A Damsel in Distress)
• After party passed fool hiding, having taken drugs
• Worked (out)