You'll have to manually configure your computer so it knows there's a 3rd tray.
Go into your Printer and Faxes from the control panel.
Right click the printer and go to properties. One of the tabs (I don't know off hand), it should be "Device Settings" or something like that, will have a list in which you can configure your printer options. It will probably say "Tray 3: Not available" so scroll down to "Installable Options", your probably have to expand it, change "Tray 3" to Installed. Next make sure at the top, where it said "Tray 3: Not Available", is now enabled and change it to Letter, Legal or whatever your Tray 3 is.
This is the only way I know, your printer may not have these options, but thought it might help. The printer I know this from is an HP as well so it should be, or at least close, to the same.