Here is a list of all the World Champions along with in which season of their career they won the title and the number of races they competed in before winning their first title.
1 Giuseppe Farina 6 - 1st Season - 6 races
2 Juan-Manuel Fangio - 2nd Season - 15 races
3 Jacques Villeneuve - 2nd Season - 33 races
4 Alberto Ascari - 3rd Season - 18 races
5 Jack Brabham - 3rd Season - 22 races (he did race once in 55 and 56 so I didn't count those as seasons!!)
6 Emerson Fittipaldi - 3rd Season - 25 races
7 Denny Hulme - 3rd Season - 26 races
8 Nelson Piquet - 3rd Season - 49 races (he raced for 5 races in 78 so I didn't count that as a season)
9 Phil Hill - 4th Season - 26 races
10 Jim Clark - 4th Season - 30 races
11 Michael Schumacher - 4th Season - 52 races
12 James Hunt - 4th Season - 52 races
13 Fernando Alonso 4th Season - 67 races
14 Graham Hill - 5th Season - 40 races
15 John Surtees - 5th Season - 41 races
16 Jackie Stewart - 5th Season - 47 races
17 Keke Rosberg - 5th Season - 51 races
18 Niki Lauda - 5th Season - 55 races
19 Damon Hill - 5th Season - 67 races
20 Ayrton Senna - 5th Season - 77 races
21 Alan Jones - 6th Season - 80 races
22 Alain Prost - 6th Season - 87 races
23 Mike Hawthorn - 7th Season - 47 races
24 Jochen Rindt - 7th Season - 60 races
25 Jody Schedkter - 8th Season - 97 races
26 Mika Hakkinen - 8th Season - 112 races
27 Mario Andretti - 10th Season - 79 races
28 Nigel Mansell - 13th Season - 176 races
So lets here's some stats

46% of World Champions win their title within 4 seasons of their debut
71% of World Champions win their title within 5 seasons of their debut
Only 29% of World Champions took more than 5 seasons to win the title and only 14% of World Champions take more than 7 seasons to win the title
FYI: this is Webber's 5th season, Button's 7th, Montoya's 6th and Raikkonen's 6th, their chances (according to historical stats) are getting smaller !!