Mainly it's the presence of water in the past, and some indication it is still there today, and may be habitable. Then indirect reasoning - that life either got to Earth or evolved here very quickly within a few hundred million years. If it can start here so quickly, perhaps it had time to get started on Mars before it lost its atmosphere and its ocean.

There’s the evidence of Allan Hills 84001 too, which though most would say doesn’t prove that the meteorite contains life, still remains compatible with life, and the meteorite shows that Mars at the time had liquid water and the temperature was suitable for life too.

Then, it depends how far it evolved. If just got to an early stage, likely to be very hard to find. If it evolved as far as photosynthesis and resistant spores etc, it may still be there to this day indeed. Or it may be something in between.

Some think that Viking discovered life on Mars. Recently that got revived with the discovery of circadian rhythms in the data that were not exactly synchronized with the Martian sols, quite hard to explain except by invoking life.

Then there are the methane plumes as well. They can be produced without life, or could be ancient methane that was produced by life originally. But some think they might be produced by present day life.

If there is life there, even today, we would not expect to be able to see it from orbit, and it may leave no signature in the atmosphere not if it is slow growing in conditions more inhospitable than the dry valleys in Antarctica - which is quite likely.

See:

• Rhythms From Martian Sands - What Did Our Viking Landers Find in 1976? Astonishingly, We Don't Know
• Are There Habitats For Life On Mars? - Salty Seeps, Clear Ice Greenhouses, Ice Fumaroles, Dune Bioreactors,...
• Will We Meet ET Microbes On Mars? Why We Should Care Deeply About Them - Like Tigers
• Why Mars Surface Life May Leave No Traces In Its Atmosphere: Our Rovers May Need To Go Up Close To See It
• Where Should we Send our Rovers to Mars to Unravel Mystery of Origin of First Living Cells?