Not sure when you would ever want to have a private conversation with a LEO when he is on duty, unless you know the guy personally. Even then, if he is doing his job while talking to you I would consider it a public conversation. If you are standing around enjoying a adult beverage together then I would lean towards it being a private conversation. If he is joining you in the enjoyment of said adult beverages that is. If he doesn't partake of adult beverages as a personal choice then it all boils down to your comfort level since LEOs are really never off duty.
542.400. As used in sections 542.400 to 542.422, the following words and phrases mean:
(5) "Electronic, mechanical, or other device", any device or apparatus which can be used to intercept a wire communication other than:
(a) Any telephone or telegraph instrument, equipment or facility,....blah blah blah; or
(b) A hearing aid or similar device being used to correct subnormal hearing to not better than normal;
(6) "Intercept", the aural acquisition of the contents of any wire communication through the use of any electronic or mechanical device, including but not limited to interception by one spouse of another spouse;
(7) "Investigative officer" or "law enforcement officer or agency",....blah blah blah;
(8) "Oral communication", any communication uttered by a person exhibiting an expectation that such communication is not subject to interception under circumstances justifying such expectation;
(9) "Person", any employee, or agent of this state or political subdivision of this state, and any individual, partnership, association, joint stock company, trust, or corporation;
(10) "Prosecuting attorney", the elected prosecuting attorney of the county or the circuit attorney of any city not contained within a county;
(11) "State", the* state of Missouri and political subdivisions of the state;
(12) "Wire communication", any communication made in whole or in part through the use of facilities for the transmission of communications by the aid of wire, cable, or other like connection between the point of origin and the point of reception including the use of such connection in a switching station furnished or operated by any person engaged as a common carrier in providing or operating such facilities for the transmission of local, state or interstate communications.
Not being a lawyer, it "sounds" to me here in Missouri that even the one person consent rule does not apply to recording voice or video with the devices that do not transmit the recorded conversation whether private or not. Then again, many states have similar language and still prosecute folks even in one person consent states when no wire communication interception has taken place.
I really like (5)b....no Bionic Woman hearing aids.