When a keylogger is suspected, it is crucial to first disconnect the computer from the network to prevent the potential exfiltration of sensitive data through the network. By isolating the computer, you stop the keylogger from possibly sending data to a malicious actor. Running an antivirus program is also important, but it should be done after isolating the computer to prevent further data leaks. Updating the antivirus definitions is a part of running the antivirus scan but it is not the first action to take if the computer is currently compromised. Checking the browser extensions could help if the keylogger was a malicious extension, but this is less likely the first step compared to disconnecting from the network due to the immediacy of data breach risks posed by keyloggers.