"Courts look at the firm's market share, but typically do not find monopoly power if the firm (or a group of firms acting in concert) has less than 50 percent of the sales of a particular product or service within a certain geographic area. Some courts have required much higher percentages."
Most anti-trust cases have historically been against companies with 90+% market share: Standard Oil, Bell Telephone, Microsoft. I'd love to see an example of a company that was found to have a monopoly with only 60% market share.