Why was 4th Hokage chosen when the 3rd was still alive and capable? A few examples:

4th Hokage: He was nominated and chosen when 3rd Hokage was still alive and was capable of fighting (courtesy: 9-tails attack on Konoha)

5th Hokage: after the Third Hokage deceased.

4th Raikage: After the Third Raikage deceased.

I thought the next Kage would only be chosen after the previous Kage's death. But that wasn't the case for 4th Hokage! Was he strong enough to be believed to take over Third? Was it because the Third believed he was too old ?

Btw, the Third continued to be Hokage after 4th was deceased!

I have never come across an info that notified the 4th Hokage's nomination..
In the wiki stands the following:


  After serving as Hokage for many years, Hiruzen started looking for a successor to the title. While he hoped to be able to give the position to Orochimaru, he saw that he only was interested for the power it offered. Though he turned to Jiraiya, Hiruzen instead named Jiraiya's student Minato Namikaze as his successor.


I found no information about why he wanted to retire, but it seems that he just wanted to retire. Additionally shortly before he died, he spoke about retirement too. 

Note that the Second Hokage chose the third before he died according to this article:


  He chose to sacrifice himself after he selected his prized student Hiruzen for the position of Third Hokage. Homura and Koharu would later become Hiruzen's advisers. After giving the title of Hokage to Hiruzen, Tobirama went off to fight the enemies where he died a noble death