THE INCIDENT in which three United Nations soldiers were killed in southern Lebanon the other day goes to the heart of the problem the international community frantically thrust upon the world body when Israel intervened in Lebanon earlier this year. To include the Israelis to withdraw, something had to be done to prevent Palestinian guerrillas from easily resuming, from southern Lebanon, the raids into Israel to whcih Israel had responded by its invasion. The United Nations, which was keeping the peace already on Israel's borders with Syria and Egypt, was hastily recruited. If people had focused sharply on the difference in Lebanon, however, one wonders whether the United Nations would have been assigned the job.

In those other places, very fine-grained agreements were worked out before the peacekeeping units were sent, and the established governments that worked out the agreements accepted responsibility for putting them into effect. In Lebanon, almost none of the detail was worked out in advance and, most important, on the Lebanese side there has been no single established authority with which Israel and the United Nations could deal. The Lebanese government's writ simply does not run in southern Lebanon; it has no army to speak of. The Palestine Liberation Organization claims to speak politically for all Palestinians, but it lacks operational control over diverse Palestinian units and individuals in the area. That is the swamp the United Nations is in.

In the incident Tuesday, Palestinians apparently not under the control of the PLO shot up a U.N. contingent. The PLO, which has vowed to cooperate in the particular matter of the safety of peacekeeping personnel, set out after the offending guerrillas. But, meanwhile, the U.N. contingent reduced its patroling, thus raising the critical question of whether it is or will become a U.N. practice to retreat under guerrilla intimidation or whether, as one must hope, the peacekeeping force was merely making a limited and temporary adjustment.

On Wednesday the Security Council reaffirmed its confidence in the peacekeeping potential by deciding to add 2,000 men to the 4,000 already on station. The fact remains that in undertaking to ensure the "peaceful nature" of the border area, the United Nations has tackled a project that the Lebanese government, the Christians of southern Lebanon and their patron, the Israelis, had not previously been able to perform. Indeed, under the best imaginable circumstances the United Nations could not expect to stop every infiltrator, given the terrain; nor to prevent guerrillas in the zone to the north from firing long-rangee guns at Israeli border villages; nor to halt Palestinian raids launched by sea from places like Tyre, a Palestinian redoubt that even the Israelis were loath to take on. In the circumstances, the Israelis have reason to want to see their nemesis, Yasser Arafat, tighten his authority over the undisciplined extremist elements in the Palestinian movement, as unwanted by Tel Aviv as the political results of that tighter control might be.

The United Nations is working on a military aspect of a problem whose essence is political. It is the Palestinian problem. No tranquillity will come to souther Lebanon, or to Lebanon as a whole, or to Israel, while the legitimate grievances of the more moderate Palestinians are unresolved. That may not offer much consolation to the U.N. forces under fire. But it should remind the parties to the peace negotiations of the perils that lie ahead if no progress toward a comprehensive Mideast settlement is made.