Recall, in Earth's history, the important time for the formation of life is
between 3.5 and 3.8 b.y.a. Might the conditions on Mars been like Earth
at this time: transient surface ponds (the organic pre-biotic soup), hydrothermal
venting near oceanic ridges and mantle hot spots? Mars probably had a
similar reducing atmosphere and plenty of CO2, just like early Earth.
Life on Mars would have the same requirements:
Did we infect Mars? We've discussed panspermia, how about bacteria-ridden rocks from Earth, hurled into space from large meteorite impacts, making their way to the Martian surface? It would take millions of years, but maybe some bacteria could survive the trip.
The Viking Missions of the 1970's did not find evidence for life at the two positions of the landers. Maybe we were unlucky? Maybe Martian life isn't like on Earth, but can survive in only specific areas, near hot springs associated with volcanism, or deep (several km) down inside the surface rock.
Perhaps life formed on Mars early on, just like it did on Earth (though we really don't know how, when or where), perhaps in a warm surface pond. But then it made its way, evolving and adapting, to more a protected, stable environment deep underground. Meanwhile, the surface of Mars become colder, dryer, lost nearly all of its atmosphere and become unable to support life anymore.
But what about DEEP below Mars surface? See here