Convert multiple input levels into number
If you used just one conductor (stripped of insulation) dangling in the water you would get an analogue current rising as the water level rose\$^1\$. This could develop a voltage across a resistor that could be digitized by an ADC (analogue to digital converter). The ADC would need probably only three IO connections namely start_convert, clock and data out i.e. two outputs and one input. You could use a 16 bit ADC and get a lot more resolution than what you currently have but, they are just numbers so having too much resolution isn't really a problem.

If you are insisting on using your original probe then use a serial to parallel encoder as mentioned in the comments but make sure that the voltage in levels are capped to a suitable voltage using a zener diode.



\$^1\$ - Disclaimer - I know nothing about how the water might ultimately eat away at this probe due to the current flowing and I wouldn't recommend either probe for use in drinking water or where the water is expected to be uncontaminated. This also applies to fish ponds - I wouldn't want to be blamed for electrocuting a prize koi carp.