It does not technically replace it but instead add an additional ability of equip-0. This means you can choose to pay 0 or you can remove a charge counter to equip it to a creature. Usually you would pay 0 of course, but there are situations where it can come up.
If you control three or more artifacts and control Puresteel Paladin, each Equipment you control gains an additional equip ability (namely "equip 0") even if it already has an equip ability or that equip ability's equip cost is 0 (as in Lightning Greaves) (C.R. 113.2c). In this case, you can still activate each such Equipment's normal equip ability (C.R. 702.6a, 703.6e). Note that under C.R. 113.2c, "each instance [of the same ability] functions independently".
EDIT (Apr. 27; Feb. 5): Add rule citation.
EDIT (Jan. 30, 2021): One rule was renumbered in the meantime.
It does not technically replace it but instead add an additional ability of equip-0. This means you can choose to pay 0 or you can remove a charge counter to equip it to a creature. Usually you would pay 0 of course, but there are situations where it can come up.
EDIT (Apr. 27; Feb. 5): Add rule citation.
EDIT (Jan. 30, 2021): One rule was renumbered in the meantime.