The 1971 war lasted only 14 days and defeat took the Pakistani populance by surprise, as previous stalemates in 1947 and 1965 were considered as evidence of Pakistani military prowess which could match India's overwhelmingly large numerical superiority. News that their Army had signed an instrument of surrender came as a shock to the people in West Pakistan who had thought that they were leading the war in the East.

After the defeat to Indian and Bangladeshi forces, not only did Pakistan lose all of East Pakistan, it was also forced to sign the Shimla Agreement while 90,000 Pakistani soldiers were being held as prisoners of war by India. The practical impact of Shimla Agreement was that the Kashmir dispute was designed as a matter to be resolved through further bilateral discussion, instead of through a plebscite as required by UNSC Resolution dated January 5, 1949.

Pakistan also fell let down by China and its western allies. The United States went as far as deploying the USS Enterprise in the Bay of Bengal where the Indian Navy's capital ship INS Vikrant was enforcing a complete blockade, but nothing further as Russia kept vetoing multiple resolutions calling for a ceasefire. A furious Zulfikar Ali Bhutto at the UN Assembly: http://www.youtube.com/watch?v=qYHUJBRRnc4

Quickly after the war, Yahya had to resign and give way to Bhutto who (convinced that he could no longer rely on external support) made his intentions clear: "If India builds the bomb, we will eat grass and leaves for a thousand years, even go hungry, but we will get one of our own. The Christians have the bomb, the Jews have the bomb and now the Hindus have the bomb. Why not the Muslims too have the bomb?"

And sure enough, the Indians went nuclear 3 years later in 1974 with the Smiling Buddha - what they called as a "peaceful nuclear explosion".

Meanwhile, Dr AQ Khan (Mohsin-e-Pakistan, the Benefactor of Pakistan), the father of the Pakistani nuclear bomb, is under investigation during his engagement as a subcontractor with Dutch company URENCO, suddenly leaves for Pakistan in 1975 with copied blueprints for centrifuges and other components and contact information for nearly 100 companies that supply centrifuge components and materials (later convicted in absentia by a Dutch court) and promptly joins Pakistan Atomic Energy Commission (PAEC). After conflicts at the PAEC, Prime Minister Bhutto gives Khan autonomous control over Pakistani uranium enrichment programs. Khan founds Engineering Research Laboratory (ERL) which focuses exclusively on developing an indigenous uranium enrichment capability. In early 1980s, Khan also acquires blueprints for the Chinese bomb that was tested in China's fourth nuclear explosion in 1966. Pakistan was suspected of having produced enough highly enriched uranium (HEU) for a nuclear weapon by the late 1980s and were by that time exchanging nuclear technology in return for ballistic missile technologies from North Korea, Libya and Iran.

Between May 11 and 13, 1998, India conducts a series of five nuclear tests. Pakistan was ready to respond with a series of its own tests on May 28 and 30.

EDIT: words

It's basically covered, but here are a few additions from an essay I wrote on a similar subject. First and foremost, Pakistan had always recognised their desire/need for a bomb and so—like the other powers who wanted one, India, South Africa, Argentine, and Brazil—never signed the Non Proliferation Treaty.

While they'd desired one for a long time, it was in 1978 that the US waived the NPT and delivered nuclear fuel to Pakistan in order to "promote stability in the area and bolster their relations with states there, particularly those that can play a role in checking Soviet expansionism" (Waltz, 1981, p.8). The use of sanctions alone hadn't done much to halt Pakistan's or India's nuclear programs, and it was better to have a balance than Indian domination of the region (I assume was the US logic). Again, following the 9/11 attacks, when support from Pakistan was needed, the remaining sanctions were lifted as a sign of good will.

"Whom most of which have publicly declared they are interested in pursuing the development of nuclear weapons."

This isn't really the case. Iran, the Arabian states, the Middle Eastern states — none of those have "publicly declared" they are interested in getting nuclear weapons. They have sometimes covertly pursued them to different degrees of intensity, but they have all signed the Non-Proliferation Treaty. At best, what some of them have done (e.g. Saudi Arabia) is hint that if other powers in the region got nuclear weapons, they might be forced to withdraw from the NPT and get some of their own. That's not at all the same thing as saying they've been interested in them, much less them having pursued them.

Saddam made an attempt on nuclear weapons some years ago, but the fact of the matter is is that totalitarian grimes can be remarkably bad at producing outcomes. In Saddams case, he put impossible deadlines on his scientists causing them to rush results. They ended up losing a lot of progress when one of their facilities exploded because of safety lapses in favor of speed. Other nations, like Iran, are not likely seeking nuclear weapons. Rather, they want to become threshold countries who can produce these weapons on short notice.