The S&P 500 index is maintained by S&P Dow Jones Indices, a division of McGraw Hill Financial. Changes to the index are made periodically, as needed. For Facebook, you'll find it mentioned in this December 11, 2013 press release (PDF). Quote:
New York, NY, December 11 , 2013 – S&P Dow Jones Indices will make the following changes to the S&P 100, S&P 500, MidCap 400
and S&P SmallCap 600 indices after the close of trading on Friday,
- Facebook Inc. (NASD:FB) will replace The Williams Companies Inc. (NYSE:WMB) in the S&P 100, and Facebook will replace Teradyne Inc.
(NYSE:TER) in the S&P 500 [...]
You can find out more about the S&P 500 index eligibility criteria from the S&P U.S. Indices methodology document (PDF). See pages 5 and 6:
Additions - S&P 500, S&P MidCap 400 and S&P SmallCap 600 Market Capitalization.
Market Capitalization - [...]
Liquidity - [...]
Domicile - [...]
Public Float - [...]
Sector Classification - [...]
Financial Viability - Usually measured as four consecutive quarters of positive as
reported earnings. [...]
Treatment of IPOs - Initial public offerings should be seasoned for 6 to 12 months
before being considered for addition to an index.
Eligible Securities - [...]
Timing of Changes
Changes to the U.S. indices other than the TMIX are made as needed,
with no annual or semi-annual reconstitution. [...]
LabCorp may have a smaller market cap than Facebook, but Facebook didn't meet all of the eligibility criteria – for instance, see the above note about "Treatment of IPOs" – until recently.
Note also that "Initial public offerings should be seasoned for 6 to 12 months" implies somebody at S&P makes a decision as to the exact when.
As such, I would say, no, there is no "simple rule or formula", just the methodology above as applied by the decision-makers at S&P.