How does a realestate agency choose which tenent to take the new house?

Went to a house inspection today, but there were a few other inspectors. Really liked the house, and have decided to take it (rent). Just want to know what the odds are for me to get it? What would the realestate agency consider when they choose the tenant?

First of all; you and the others are NOT "inspectors" and you are not "inspecting" the house unless you are qualified to do home inspections. You are a possible tenant looking to rent the property. And you should not be dealing with a real estate agency; you may be having a Realtor show you houses but the final decision will be or SHOULD be made by a property management company.
How they choose a tenant to lease a property is that they try to find the best tenant for the property to protect the best interest of the property owner and who they think will have the lower risk of either not paying rent or causing damage to the property. In this attempt to qualify tenants they will look at employment history, income , credit report, past rental history, if there are any pets, number of people living at the house, etc.