It's not simply what I think, rather it is a geopolitical eventuality.
Both Iran and Pakistan are rising powers, Pakistan more so than Iran, and both are located in the same region. A geopolitical clash is inevitable. They may not have any territorial disputes, but they do have a number of other disputes, just look at Iran constantly shelling Pakistani territory.
As both Iran and Pakistan grow economically, they'll have no choice but to expand their geopolitical footprints, just like how every other growing power has.
India is, honestly, not really a part of the equation here. Iran's Chabahar is practically on hold; despite India's promises of funding and manpower, India's extreme bureaucracy has slowed down progress to a crippled crawl. Also, no doubt Iran is also worried about India using Iranian territory as a launching pad for spying and terrorist operations against neighboring nations, so we can expect to see Iran show reluctance to cooperate with India in this regard, lest it ends up angering its immediate neighbor, especially considering how easily Indian spies are caught.
So, like I said, Iran and Pakistan have other issues which will likely cause tensions between the two. Iran may have been an ally during the Shah's rule, but he wasn't exactly deposed for nothing. After his disposal, let's never forget that the new Iran, and KSA fought a proxy war in Pakistan, leading to today's sectarian issues.
Always keep in mind, there are no permanent friends, there are only national interests.