Good question!

Following the end of the Yom Kippur War, and through US-mediated negotiations, the Egyptians and Israel concluded a pact signed on September 4, 1975, often referred to as "Sinai II". It effectively solidified nonaggression as a concept, and created a principle that both sides would work towards mutually resolved conflict without the use of force. It also established military zones and armistice lines with early warning stations and buffers.

Assad in Syria, unlike Sadat in Egypt, changed few of his views. His own agreements bore far less fruit, and didn't seem to be going anywhere. In this sense, it was partly down to personality and the leadership of both states: Assad was far more stubborn and hard-line on Israel than Sadat. This is reflected further in how the two peace paths developed.

Despite the collapse of peacemaking following Nixon's resignation and Watergate, peace with Egypt never really died as an idea. Sadat seemed very much to be in favor of peace, and President Carter was likewise interested in it. Carter had little foreign policy experience and was more friendly toward Arab states than Nixon in the context of the conflict, so an opportunity opened for Sadat. Carter still believed, as did much of the US foreign policy establishment, that peace still required more than Sadat. He and his Secretary of State tried to get negotiations going for a wider meeting in Geneva for peace, but plans for that were confused by the win of right-wing Menachem Begin in Israel in 1977. For the first time in Israel's history, a right-wing leader had risen to lead Israel, and Carter was unsure how to respond. This was in large part due to the failure of Israel in response to the Egyptian and Syrian attack in the Yom Kippur War; despite success near the end, the war was viewed as a failure and ruined the left-wing Labour party's hold on the country.

Begin was significantly more clear in claiming the West Bank and Gaza were part of Israel, in his view. He called them "as Jewish as Tel Aviv". Relations between him and Carter got off to a bad start almost immediately, over settlement construction.

Behind the scenes, however, Israel was doing more diplomatically. Israel, through both Romania and Morocco (Begin spoke to Romania's President, Israel's Moshe Dayan flew to Morocco to talk to the King) asked to pass a message to Egypt supporting a meeting and peace. Morocco arranged for a meeting between Dayan and Egypt's deputy PM, and peace became a possibility.

Sadat's opening offer said peace was possible, but only if Israel withdrew from the Sinai, Gaza, West Bank, Gaza, and East Jerusalem. This was not going to happen from Israel's perspective, but Israel allegedly (this has been questionably confirmed) offered to withdraw from the Sinai for peace.

Sadat, noting he couldn't get much more out of the US than slightly more favorable rhetoric, and knowing Israel appeared to be willing to at least give up the Sinai, eventually made his famous offer to fly to Israel to speak to Israel's Knesset. Negotiations effectively took off from there. Much of this was because of the force of Sadat's will to make peace, and his personality.

What happened to Syria, then?

Well, Assad was more stubborn by far. Sadat believed that if he made peace with Israel, Syria and Lebanon and Jordan would follow. He figured they'd even join before the process concluded, and while it was going on.

Instead, Syria reacted with anger. They had worse relations with Egypt following Sinai II, and Assad had a day of mourning declared nationally following Sadat attempting to convince him to join him in going to Jerusalem (or at least to approve publicly of the trip). This makes sense; crowds gathered to denounce Sadat in Iraq, and Sadat faced government turmoil over these decisions, and Syria didn't appear willing to follow in his footsteps. In short, the reason Syria was left out is because they refused to be part of it, and despite attempts to organize a more multilateral peace conference, Syria rebuffed overtures.