Light switch replacement

I have wired a few light switches, but this one set has me stumped (prior home owners work was questionable). Two light switches, both single light controls (at least as far as the light switch design shows). 2 wires coming in. No ground as this is an older home. Best guess is that power is starting at the light and coming down to the switch. The confusion is 1 of the white wires is not being used. The other black goes to the right switch. The other black wire that comes in is from the other switch. The other switch has a white and black coming in, the black wire is shared with the other switch. I want to replace the switches with updated fixtures, but safely. What wires should go where?