What is the difference between 覺得 and 想？
As you learned from dictionaries, 想 and 覺得 have meanings that are not overlapped. 

When it comes to the overlapped meaning 'think', the different between 想 and 覺得 are as below:

"我[想]机会不是很大" - "I [think] the chance is not great" (thinking mainly base on imagination/ judgment; mostly a prediction) 

"我[覺得]机会不是很大" - "I [think] the chance is not great" (thinking mainly base on feeling; mostly a hint/ feeling)

Both '想' and  '覺得' describe 'expressing opinion' , but with different base. If you what  to emphasize the opinion is base on judgment after some consideration, you should use '想'; If you what  to emphasize the opinion is base on a hint or some feeling, you should use '覺得'

More example:

我(想)德國隊會赢 - in your judgment, team Germany will win (base on the past record and the skill level gap between the two teams)

我(覺得)德國隊會赢 - you personally feel Germany will win (just a hint, because they seem like a winner)