Ok. I have done a little research and what you need depends on the types of monitors you are using.
*Short Version*
If you have at least 1 monitor with a DisplayPort connection, connect it with that port and you can use passive adapters as needed.
If you do not have any monitors with a DP connection, you will need at least 1 active adapter to convert the required DP signal to whatever it is you need.
*Long version*
To use Eyefinity with more than 2 monitors (3 in your case) at least one of them will have to using a DisplayPort signal. If the monitors themselves do not have a DP port, then you will need an ACTIVE adapter as the card will have to output at least 1 DP signal which will then have to actively be changed to a legacy signal (HDMI, DVI, VGA).
If you are using Eyefinity and at least one of the monitors has DisplayPort, then simply connect it directly to one of the DP ports on the card. It will satisfy the requirement of one DP signal. If you then use a second DP port for one of the other two monitors via an adapter, it can be a PASSIVE adapter since the signal will be legacy signal over a DP connection.
AMD seems to be using DisplayPort secondary clock being activated as a trigger to identify an Eyefinity setup. On the legacy ports, a single clock can only drive two monitors max, so all additional connections have to use a DP signal and its clock.