Condition 3 requires that S's reasons for believing p must be truth-connecting, non-coincidental, pertinent, or applicable (i.e. relevant) for why p should be believed true, and includes no normative element for its potential satisfaction. The evidence that is 'relevant' for why p should be believed true, is presumed objective and independent of persons.

Believing a true proposition constitutes knowledge only if believing is properly linked to evidence that makes it true. Persons and animals can believe (and know) p upon an unconscious exercise of a cognitive ability such as perception. Persons being better cognitively developed can believe p from explicit argument or explanation. Condition 3 and the PE definition makes no claim about how much relevant evidence is 'adequate' to believe p, and this doesn't imply S needs to be conscious of (or be able to recount) the reasons for believing p, except in situations of critical doubt.

There are two senses of 'relevant' found in ordinary and philosophic language. The following example about how a person can possess relevant reasons for knowing the causal mechanisms behind a particular event will make clear the sense of 'relevant' that is being used in condition 3. The particular event is that of a house fire.

Suppose that a house in a residential neighborhood is substantially damaged by a fire. The cause of the fire is initially unknown. Local fire investigators are called in to determine 'why did the fire start?' Pre-theoretically, we believe that there are relevant reasons for why a house catches on fire. We don't believe that a house suddenly combusts without a cause. When seeking the cause(s) for why a fire started, fire investigators want to discover whether an arsonist was involved, or if there was careless smoking, or whether there was an electrical problem, or something on the stove ignited, or a lit candle accidentally fell, or lightening struck and so on. In order to obtain knowledge of the cause, the investigators seek objectively relevant evidence and relevant reasons for why the house caught fire, and wish to discard any extraneous irrelevant states-of-affairs not associated with the cause of the fire. 

Let us suppose fire investigators offer this final report that explains why the fire started:

1. An upended candle was found in the bedroom of the home, where most of the fire damage occurred.
2. The pattern of how the fire spread, and resulting damage suggests that the fire started in the bedroom near the fallen candle.
3. A resident of the home admits having left a candle burning while leaving the home several hours earlier, and
4. There is no other evidence (indicating arson, electrical problems, careless smoking, lightning etc.) which suggests that anything other than unattended lit candle was the cause of the fire.
5. Therefore, p: The fire was caused by an unattended lit candle that apparently fell and ignited surrounding combustible materials.

Whether the four premises given by the investigators for why the fire started are actually 'relevant' for why the fire started is not something we decide.  In other words, the relevant reasons for why the house caught fire are truth-connecting, objective, and independent of us.  The objectivity of relevant evidence is commonly presumed by physical scientists (e.g. physicists, chemists, and medical researchers) who seek the relevant causal factors for why certain physical phenomena occurs.

The sense of 'relevance' used in condition 3 is consistent with a standard dictionary sense.
The meaning of ‘relevant’ in condition 3 is consistent with the dictionary definition: ‘relevant’ (adj.) means ‘bearing on the matter at hand, germane, material, applicable, pertinent.’  To understand condition 3, it must be remembered that the ‘relevant’ premises for why any empirical p should be believed, are objective.    

Another sense of 'relevance' not being used in condition 3.
There is another sense of ‘relevant’ that is not being used in condition 3.  It is sometimes said (in ordinary language) that what counts as ‘relevant evidence’ is any evidence that is ‘somehow related’ or ‘might have some significance’ for why p is true or false. For instance, at the beginning of their inspection, fire investigators will be interested in any evidence that may have a bearing on why a fire started.  In this sense of ‘relevant’ all physical evidence (e.g. the condition of the electrical system, the possibility of arson, etc.) that might have some significance is ‘relevant’ to determine the cause of the fire.  This wide sense of ‘relevant’ is not the sense used here. 

Narrow sense: The 'relevant' evidence for why p is true, is an explanation that is objective (and truth-connecting) for why p is true. The evidence 'relevant' for why p is true, is not something we decide.

Wide sense: The 'relevant' evidence for why p is true, is any evidence that might conceivably be related to the truth or falsity of p. The evidence that is 'relevant' for why p is true, is subject to pragmatics and probabilities.