If you're wanting general information about probing, I suggest you start with part one.
This guide deals with probing and information regarding probing during combat restricted to a single system. This usually occurs during strategic ops with a reinforcement timer expiring shortly.
149,597,870.7Km = 1AU
299,195,741.4Km = 2AU
448,793,612.1Km = 3AU
598,391,482.8Km = 4AU
747,989,353.5Km = 5AU
897,587,224.1Km = 6AU
1,047,185,095Km = 7AU
1,196,782,966Km = 8AU
1,346,380,836Km = 9AU
1,495,978,707Km = 10AU
1,645,576,578Km = 11AU
1,795,174,448Km = 12AU
1,944,772,319Km = 13AU
2,094,370,190Km = 14AU
2,147,483,647Km = 14.355AU
1,000,000 kilometers = disconnect range (if a person logs off outside a station/pos the game puts them at this distance until they disappear).
Directional scan, or dscan henceforth, is a very useful tool for scanning down hostiles. Dscan deals with kilometers (km) while most of the overview deals with Astronomical Units (AU). The maximum dscan range is 2,147,483,647 kilometers = 14.3550415 Astronomical Units. I prefer to just think 14.5 AU as it's easier to remember.
Why is this useful?
You can set your dscan to 1,000km and constantly press it until you see hostiles starting to show up. Depending on your skills hitting analyze at that time might return a result on them as they land on grid.
Dscan also offers a large radius scan with very little delay, though it does not indicate an exact location nor allow you to warp to it. Dscan does indicate if something is ongrid or offgrid with you as seen here:
As this picture illustrates, I am on-grid with one tower, but there is a second tower and a jump bridge in system as well. These are not at the same location as myself, hence the lack of distance. This works in combat as well. Assume that your fleet is fighting against a hostile Loki fleet, and this fleet is probably receiving boosting from another Loki. Your probes are positioned at 0.5 AU, and the only results you are seeing are the Lokis on-grid. With a 360 degree dscan, you notice a Loki with no distance listed. You have two options: immediately expand your probes to 8 AU, or change the dscan range to half. To do this, change the 2 to 1 - while not exactly half, speed factors in as well. If that Loki disappears from dscan after this change, it means he is over 7 AU away, but within 15 AU. If the Loki remains on dscan, it means he is within 7 AU of you.
You are then able to either start scanning with your probes, or attempt to get a better fix on the Loki by adjusting your scan direction. With the changes to deep safes, it is safe to assume that the Loki will be somewhere within the path of celestials:
Once you have figured out approximately where the Loki (or whatever target) is, move your probes into that area and start scanning. Start with 8 AU and decrease around the target as you get results. Results will be shown as either a red square, which means more than one probe got a hit, or a large red circle which means only one probe got a hit. Practice this skill until you're able to interpret the results and can find the ship in only a few scans. Note: most boosting Lokis will have ECCM running and will be impossible to get a 100% result on without perfect skills and implants.
Differentiating between Friendlies and Hostiles
Easiest option: Ship types. If your fleet is in battleships and the hostiles are in battlecruisers, change your filter to only show battlecruisers.
Distance: If the friendly and enemy fleet are both in battlecruisers, sort your scan results by range and ignore the results that are the same as the friendly fleet. Issues arise if both fleets are at the exact same distance from you.
Location based: If your fleet comes in from a gate, while dropping and formatting probes, hit analyze on your fleet and ignore them ahead of time. If you're already in system and a friendly fleet enters from either a gate or a cyno, place your probes there and ignore those results.
Unique ship based: If both fleets are fighting on the same grid, while your fleet is offgrid attempting to enter the fight. Example: both fleets are in AHACs, you know your doctrine does not use Guardians, you see them on your scan results by sorting by ship type. You can then warp to that Guardian and start engaging the hostiles.
In the Heat of the Battle
Combining dscan, probing and intel you are able to chase hostiles to their safes. Visually seeing the direction the hostiles warped allows you to position your probes and have your fleet align. Getting assistance from your fleet can make probing faster if you did not see which direction the hostiles warped.
Use probes to dictate range. A target needs to be over 150km away from you to warp to it- but that does not mean you need to warp 150km. If the hostiles are 200km away from your close range fleet, warping to them at 0km is a good choice. If you are in sniping ships or longer ranged ships than your hostiles you can choose the range to warp to them. Use your overview to see the direction the hostiles are moving and their speed. Changing your warp distance may be beneficial.
An example: the hostile fleet has an effective range of 40km, your fleet operates best between 50 and 75km. The hostiles are MWDing directly away from you at 3km/s starting at 200km. Assume it takes around five seconds from when you initiate warp fully aligned to when you are able to target and fire. If you fleet warp at 50km (the beginning of your advantage), by the time you have exited warp and start locking, the hostiles will now be 65km away [50 (initial warp) + 3 (kilometers per second) x 5 (seconds it takes to warp)] and out of your range within a few seconds. Knowing this, if you were to have warped to the hostiles at 35km, by the time you exited warp you would have been at perfect range.
EVE is not static. The likelyhood of the above situation occuring exactly is quite small. It is difficult to attempt to give examples in fixed settings, as the game is not a fixed environment. Combat probing is a learned skill and can only be improved through practice. Hopefully these tips can help you understand how to use the many features in EVE in conjuction to be a better prober and fleet commander.