Assuming both survive, but the battle is still a stalemate, the easy answer is that the war will continue. Probably though Cleon is recalled to Athens and Brasidas to Sparta, the lack of a victory having weakened the pro-war factions in both cities.
The key to the future of the conflict IMO is how Cleon's survival affects Athens' domestic politics. If Cleon and Alcibiades cooperate, then the pro-war faction will dominate. If they Alcibiades doesn't side with Cleon, then Athens policy is unsettled. IMO, Cleon will have to reassert his authority, but he probably manages it. Athens launches an expedition against Melos or the like (an non-subject state in the Aegean) which gives Cleon time to recoup his support.
Sparta meanwhile has to deal with the captive from Pylos and the Athenian fort on Sphacteria. She probably asks for peace, but Cleon manages to get it rejected (this where Alcibiades' loyalites are key, though). Athenian strategy is then two-fold: seek an alliance with Argos and expand forward-fortification from bases around Pylos and Sphacteria. I'd expect that the later occurs first, around 420ish. The prisoners and an eventual Athenian alliance with Argos prevents any Spartan invasion of Attica.
If Athens takes too long, Sparta sends envoys to Persia and even to Sicily trying to find more allies and essentially a navy to attempt to force Athenian subjects to revolt. I doubt Persia is receptive, since Sparta looks more desperate. Sicily is still making do with the declaration of the Congress of Gela, though the situation in Leonitine and Segesta may invite involvement as per OTL.
Athens meanwhile probably focuses on two fronts; without OTL Mantinea and the oligarchic coup at Argos, there's still an active front against an active beligerent so there's no need or pretext for the Sicilian Expedition. Most likely Cleon is looking for a battle in the central Peloponnese or a battle around Corinth. Either way, with Argive support strong and with strong Athenian support for the Argive alliance, Athens has a fair chance of scoring a victory over a Peloponnesian force in a pitched battle. If so, Sparta probably makes a separate peace, but Thebes and Corinth try to fight on. If Sparta manages a victory, it's probably ephemeral as long as Cleon remains in control of Athens. Cleon probably has an easy side besting Nicias while Alcibiades has an incentive to support aggressive schemes in order to find a path to glory.