row.names  1    2     3   ...          row.names  1    2   3  ....

A          0.1 0.2 0.3                   A        1    1   1
B          0.4 0.9 0.3                   B        2    3   1
C          0.9 0.9 0.4                   C        1    3   1
.

X  S   CONF P
1  A   0.1  1
1  B   0.4  2
1  C   0.9  1
2  A   0.2  1
2  B  ......

out <- data.frame(X = rep(colnames(conf), each = nrow(conf)),
                  S = rep(rownames(conf), ncol(conf)),
                  CONF = c(conf), P = c(P))
out
#   X S CONF P
# 1 1 A  0.1 1
# 2 1 B  0.2 1
# 3 1 C  0.3 1
# 4 2 A  0.4 2
# 5 2 B  0.9 3
# 6 2 C  0.3 1
# 7 3 A  0.9 1
# 8 3 B  0.9 3
# 9 3 C  0.4 1

cbind.data.frame(X = rep(colnames(conf), each=nrow(conf)),
                   S = rep(rownames(conf), times=nrow(conf)),
                   CONF = matrix(t(conf), ncol=1),
                   P = matrix(t(P), ncol=1))

conf <- matrix(
  c(0.1, 0.4, 0.9,
    0.2, 0.9, 0.9,
    0.3, 0.3, 0.4),
  ncol=3, byrow=T
)
rownames(conf) <- c("A", "B", "C")
colnames(conf) <- 1:3

P <- matrix(
  c(1, 2, 1,
    1, 3, 3,
    1, 1, 1),
  ncol=3, byrow=T
)
rownames(P) <- c("A", "B", "C")
colnames(P) <- 1:3

library(reshape)
conf <- cbind(as.data.frame(conf), "S"=rownames(conf))
P <- cbind(as.data.frame(P), "S"=rownames(P))
out <- merge(melt(conf, id="S"), melt(P, id="S"), by=c("variable", "S"))
colnames(out) <- c("X", "S", "CONF", "P")