Till 1971, Pakistan has invaded India 3 times and lost every time. In 1971 war, they realized that even sympathetic super power with a friendly leader (US under Nixon) will not commit to full fledged war where the risk of damage is high (USSR involvement).

After Pakistan lost almost half of its country (Bangladesh) in 1971 war. Even the dreamers has lost of winning a head on war.

Pakistani army & political leaders turned to serious investment in proxy war. In mid 1970s Bhutto asked ISI/Army to engage in support and build up of factions in Afghanistan, to replace a neutral Afghan govt with a pro-Pakistani govt. USSR's invasion gave a perfect impetus to build a rebel network.

Pakistan army then used Afghanistan leanings to support militancy in Punjab. And after USSR's departure from Afghanistan used Afghan jihadis to fight against India in Kashmir.

Due to significant gap in economic progress since late 80s, Pakistani army is losing its relative strength against India. So, the chance of a direct invasion is negligible. And proxy war through terrorists and mafia would continue to be the modus-operandi for foreseeable future.

Nuclear arsenals did not become a factor till much later.

India tested its first nuclear weapon in 1974, just 3 years after the 1971 war between the two countries.

Pakistan did not test its first nuclear weapon till 1998 in response to the second nuclear tests that India conducted.

Considering that the Pakistani test was within 17 days of the second Indian test, it can be safely assumed that Pakistan had nuclear weapons for some time before that. It however is not publicly known how long Pakistan had a nuclear weapon before the test. At best we have some anecdotes about Gen Zia ul-Haq of Pakistan mentioning a Pakistani nuclear weapon in the late 80s.

Even if we assume that Pakistan had a nuclear weapon by late 1980s, that leaves a long time during which India had a nuclear weapon while Pakistan did not. Nuclear weapons therefore did not play much of a role in keeping the peace. The relations after the 1998 tests however are a different bag and are out of scope of this sub.

Political pressure from the world powers would have played a bigger role in keeping the peace, as was the internal power struggle that Indira Gandhi was going through in India.

To be honest there was still quite a good deal of conflict and hostility between the two states, like the siachen glacier incident in 1984 and operation tupac in 1988. Large scale conflict between the two actors also happened via other mediums; Pakistan would use religious fundamentalists and even kashmiris to create conflict with India. This would all build up to the eventual nuclearization of the conflict.

India with all this antagonism that came from Pakistan especially through the continual breach in sovereignty would see the rise of Hindu nationalism through the bjp. The bjp due to the past history of emasculation by the colonial masters would hence see nuclear weapons as a means to legitimize their personal beliefs. Pile on the fact that the kashmiri insurgency was an international embarrassment for India, this would make them more interested in getting nuclear weapons. As for Pakistan their history of having a military junta would make them more ameenable to having arms especially when India had them. Plus various defeats at the hands of India be it politically at the 1960 Indus waters treaty or the 1971 war meant that it was even more important to preserve state pride in order to secure the rule of the army.

At the base of it the nuclearization of the conflict really stems from the British disengagement of the area and the crude way through which it bifurcated British India and created such opposing national identities. The clash between forming a secular national identity and one based on religion would create tensions between the two states as it would seem integral to undermine the other in order to be politically relevant.

However the 1971 war was a major catalyst. It brought the anger between he two states to a new high. Firstly because it brought in other actors like the cold war superpowers which merely served to increase the aggression of the two states. Secondly because it called the Muslim identity of Pakistan into question. Having the world see that the universal brotherhood of Islam didn't work out through the mistreatment of the east Pakistanis undercut the state's fundamentals. And India's intervention in it through the funding of seccesionist group the Mitro bahani would naturally exacerbate pre existing tensions. This military defeat would spark a trend of military dictatorships in order to play to anti Indian sentiment. These dictatorships being highly nationalistic would also mean more active hostility in Pakistan's part.

So while the 1971 war was no doubt important, it exists as merely a catalyst.