A key element in praying is to be able to identify with the person one is praying for. This begins in the general level that whoever we're praying for is human, as we are. Being human means being an eikon of God, or, made in his image. With that is the potential of becoming like Jesus, no less. Also being human involves being broken in our lostness from God's goal for us as humans. This is a lostness that is moral- in us being sinners. And with that come consequences because of the soul and systemic damage that sin brings with it, in its wake/path.
The Old Testament priests are said, in the New Testament book of Hebrews, to have been able to sympathize with the people they represented to God, since they too were beset with human weakness and sin. Jesus, unlike them, is holy, undefiled and separated from sinners. But like them, he too was/is completely human. He too, was tempted in all points like us, yet without sinning. So Jesus too, is able to empathize with us humans. To help us in our weakness, as we call to him. And because of his work for us, here on earth, he intercedes/prays for us, his brothers and sisters, now.
We are told in Scripture, as those in Jesus, to rejoice with those who rejoice and weep with those who weep- in the Jesus community. We are to identify ourselves especially with our brothers and sisters in Jesus. And also with the entire human race. We certainly see this with Jesus, who became like us as a human, and then took the sins of the world on himself in his sacrifice for humankind. He lived with his disciples and loved them to the end, and called Judas Iscariot "friend", to the end. And he wept over Jerusalem, since it refused God's kingdom coming- in him.
To really pray in interceding/petitioning God for another, it is good to have a sense, wrought in us, by the Spirit, through knowledge and experience, of an identification with the person we're praying for. So that we, by the Spirit, really love another, as we love ourselves. So that we have genuine empathy that is expressed with deep concern in prayer, and praise and thanksgiving when prayers are answered.
Jesus, Thank you for becoming one of us. Even taking on yourself our sin in the mystery of your redemptive work for us. Let us be those, who are like you, taking on ourselves the woes, including failures and sufferings of others. Draw us into this, for your glory. Amen.