Uber said on Wednesday that it had raised $3.5 billion from Saudi Arabia’s Public Investment Fund, the kingdom’s main investment fund, in one of the largest-ever investments into a privately held start-up. The money was part of the ride-hailing giant’s most recent financing round and continued to value Uber at $62.5 billion. The investment, which was months in the making, does not cash out any of Uber’s existing investors. Uber, which has viewed the Middle East as an important area in its expansion, said the investment further aligned the company with Saudi Arabia as the kingdom planned to transform its economy, reducing its dependence on oil and improving employment.