Connecting new ceiling light in 1970 house
My guess is one of the cables is a switch loop the other one is a 2nd light, and the hot you know.
I would check the not hot cables with an ohm meter looking at the black white resistance with the switch in the on position one or both of the dead cables will short or very low resistance depending on the type of lamp in the other fixture, now turn the switch off check both again the cable that was shorted and now reads open is a switch leg.
The black hot goes to the white of the switch leg usually a wire nut. The black coming back from the switch is the switched hot that you connect the other dead cable black to with the new lamp black the cable that had the hot also has a white this the neutral you connect the new light white to this white and the other dead cable white together.
This will properly connect your lights. There should be some bare ground wires in the box they should all be tied together and bonded to the box it looks metal, if conduit that may be your ground instead of a bare ground.