That's an old amphenol 4 pin connector. Here is how you wire it to a 1/4" and XLR.
Pins 1 and 2 of this connector are the high impedance output. Pin 2 is the hot. To wire this output for a quarter inch connector, connect pin 1 to the sleeve (ground or shield) and pin 2 to the tip of the connector.
Pins 3 and 4 are the low impedance balanced output. Pin 4 is the plus, pin 3 is the minus, and Pin 1 is the ground or shield.
So just chop off that old connector (which I must say, I've never seen one like that, maybe someone else here can tell ya what it goes to) and put on either a 1/4" or XLR, depending on what you want to use the mic for.