Iran clearly desires to have Nuclear weapons, so does North Korea. Possession of Nuclear Weapon deters an enemy on engaging a war. Why isn't Saudi Arabia which has the third largest Military Budget desire Nuclear Weapons?
Several reasons come in my mind:
Saudis know that the USA won't tolerate any nuclear country in the proximity of Israel. Saddam and Gaddafi tried and fell victim of US rage. Iran is trying or tried in futility.
Saudis are actually under US protection. Going nuclear will create trust deficit and will call the demise of monarchy which the house of sauds are scared of.
Finally, it is speculated that Saudis financed Pakistani nuclear program and Pakistan is ready to ship nuclear weapon to Saudis at any moment and on demand.