They would find a business that was making a lot of profits and charge a slightly lower price than their competitors. In industries where price makes a significant difference (think Wal-Mart), a competitor might respond by lowering their price as well. You would have no choice but to respond by lowering your prices again. Eventually, in this scenario, you and your competitors will all drop your prices so low that there is no more profit to be made each of you is only covering his or her costs. Competition would have created a situation where there is no economic profit.
In the real world, there are startup costs and information is limited. This axiom of urban economics says that we're trying to live out the hypothetical scenario anyway we guess at what profits might be and wherever profits are found, new businesses with lower prices drive down the prices and the profits for the industry. The result is efficient for consumers, who can buy what they want at optimal prices.